From: Hamed Gorjiara <hgorjiar@uci.edu>
Date: Thu, 6 Sep 2018 20:57:56 +0000 (-0700)
Subject: Bugfix for Sudoku solver + Using Glucose instead of Pycosat
X-Git-Url: http://demsky.eecs.uci.edu/git/?a=commitdiff_plain;h=457ddef68a9d8645a925201aafb28a3c144b34df;p=Benchmarks_CSolver.git
Bugfix for Sudoku solver + Using Glucose instead of Pycosat
---
diff --git a/sudoku-csolver/.gitignore b/sudoku-csolver/.gitignore
index 648641e1..ae149edf 100644
--- a/sudoku-csolver/.gitignore
+++ b/sudoku-csolver/.gitignore
@@ -1,9 +1,11 @@
numpy*/
pycosat*/
bin/
-solved/
+solved/*
csolver
*.class
*.so
*.pyc
+*.in
+*.out
diff --git a/sudoku-csolver/Sudoku.py b/sudoku-csolver/Sudoku.py
index d84b126b..676425d2 100644
--- a/sudoku-csolver/Sudoku.py
+++ b/sudoku-csolver/Sudoku.py
@@ -1,4 +1,4 @@
-import pycosat
+import glucose
import sys, getopt
import time
import numpy as np
@@ -154,12 +154,13 @@ def sudoku_clauses():
# for all cells, ensure that the each cell:
for i in range(1, N+1):
for j in range(1, N+1):
- # denotes (at least) one of the 9 digits (1 clause)
- res.append([v(i, j, d) for d in range(1, N+1)])
# does not denote two different digits at once (36 clauses)
for d in range(1, N+1):
for dp in range(d + 1, N+1):
- res.append([-v(i, j, d), -v(i, j, dp)])
+ res.append([ -v(i, j, dp), -v(i, j, d)])
+ # denotes (at least) one of the 9 digits (1 clause)
+ res.append([v(i, j, d) for d in range(1, N+1)])
+
print "First one :" + str( len(res))
def valid(cells):
@@ -197,10 +198,11 @@ def solve(grid):
# Print number SAT clause
numclause = len(clauses)
print "P CNF " + str(numclause) +"(number of clauses)"
-
+# for c in clauses:
+# print c
# solve the SAT problem
start = time.time()
- sol = set(pycosat.solve(clauses))
+ sol = set(glucose.solve(clauses, N**3))
end = time.time()
print("SUDOKU SAT SOLVING TIME: "+str(end - start))
diff --git a/sudoku-csolver/csolversudoku.py b/sudoku-csolver/csolversudoku.py
index f61a040c..ac1fef63 100644
--- a/sudoku-csolver/csolversudoku.py
+++ b/sudoku-csolver/csolversudoku.py
@@ -14,8 +14,19 @@ def replaceWithElemConstOptimization(elemConsts, problem, sudoku):
for j, cell in enumerate(row):
if cell != 0:
problem[i][j] = elemConsts[cell-1]
+
+def constantCellConstraint(csolverlb, solver, elemConsts, problem, sudoku):
+ for i,row in enumerate(sudoku):
+ for j, cell in enumerate(row):
+ if cell != 0:
+ csolverlb.addConstraint(solver, generateEqualityConstraint(csolverlb, solver, problem[i][j], elemConsts[cell-1]))
-
+def generateEqualityConstraint(csolverlb, solver, e1, e2):
+ equals = csolverlb.createPredicateOperator(solver, c_uint(ps.CompOp.SATC_EQUALS))
+ inp = [e1,e2]
+ inputs = (c_void_p*len(inp))(*inp)
+ b = csolverlb.applyPredicate(solver,equals, inputs, c_uint(2))
+ return b
def extractItemInSetOptimization(csolverlb, solver, sudoku, N):
sets =[ [[i for i in range(1, N+1)] for i in range(N)] for i in range (N)]
@@ -48,13 +59,10 @@ def generateSudokuConstraints(N, sudoku = None, serialize=False):
s1 = [ i for i in range(1, N+1)]
set1 = (c_long* len(s1))(*s1)
s1 = csolverlb.createSet(solver, c_uint(1), set1, c_uint(N))
- problem = np.array([[csolverlb.getElementVar(solver,s1) for i in range(N)] for i in range(N)]) if sudoku is None else extractItemInSetOptimization(csolverlb, solver, sudoku, N)
+ problem = np.array([[csolverlb.getElementVar(solver,s1) for i in range(N)] for i in range(N)])# if sudoku is None else extractItemInSetOptimization(csolverlb, solver, sudoku, N)
elemConsts = [csolverlb.getElementConst(solver, c_uint(1), i) for i in range(1, N+1)]
- # Is it a sudoku to solve?
- if sudoku is not None:
- replaceWithElemConstOptimization(elemConsts, problem, sudoku)
-
+
def valid(cells):
for i, ei in enumerate(cells):
for j, ej in enumerate(cells):
@@ -72,32 +80,32 @@ def generateSudokuConstraints(N, sudoku = None, serialize=False):
# ensure each cell at least has one value!
- for i,row in enumerate(problem):
- for j, elem in enumerate(row):
- constr = []
- for econst in elemConsts:
- s1 = csolverlb.getElementRange(solver, elem)
- sconst = csolverlb.getElementRange(solver,econst)
- d = [s1,sconst]
- domain = (c_void_p *len(d))(*d)
- equals = csolverlb.createPredicateOperator(solver, c_uint(ps.CompOp.SATC_EQUALS))
- inp = [elem,econst]
- inputs = (c_void_p*len(inp))(*inp)
- constr.append( csolverlb.applyPredicate(solver,equals, inputs, c_uint(2)))
- b = (c_void_p*len(constr))(*constr)
- b = csolverlb.applyLogicalOperation(solver, ps.LogicOps.SATC_OR, b, len(constr))
- csolverlb.addConstraint(solver,b);
+# for i,row in enumerate(problem):
+# for j, elem in enumerate(row):
+# constr = []
+# for econst in elemConsts:
+# s1 = csolverlb.getElementRange(solver, elem)
+# sconst = csolverlb.getElementRange(solver,econst)
+# d = [s1,sconst]
+# domain = (c_void_p *len(d))(*d)
+# equals = csolverlb.createPredicateOperator(solver, c_uint(ps.CompOp.SATC_EQUALS))
+# inp = [elem,econst]
+# inputs = (c_void_p*len(inp))(*inp)
+# constr.append( csolverlb.applyPredicate(solver,equals, inputs, c_uint(2)))
+# b = (c_void_p*len(constr))(*constr)
+# b = csolverlb.applyLogicalOperation(solver, ps.LogicOps.SATC_OR, b, len(constr))
+# csolverlb.addConstraint(solver,b);
#ensure each cell at least has one value
-# for i,row in enumerate(problem):
-# for j, elem in enumerate(row):
-# csolverlb.mustHaveValue(solver, elem)
+ for i,row in enumerate(problem):
+ for j, elem in enumerate(row):
+ csolverlb.mustHaveValue(solver, elem)
# ensure rows and columns have distinct values
for i in range( N):
- valid(problem[:,i])
- valid(problem[i,:])
+ valid(problem[:,i])
+ valid(problem[i,:])
# ensure each block has distinct values
root = int(N**(0.5))
@@ -105,7 +113,14 @@ def generateSudokuConstraints(N, sudoku = None, serialize=False):
for i in collections:
for j in collections:
valid([problem[i + k % root, j + k // root] for k in range(N)])
+
+ # Is it a sudoku to solve?
+ if sudoku is not None:
+# replaceWithElemConstOptimization(elemConsts, problem, sudoku)
+ constantCellConstraint(csolverlb, solver, elemConsts, problem, sudoku)
+
+# csolverlb.printConstraints(solver);
#Serializing the problem before solving it ....
if serialize:
csolverlb.serialize(solver)
diff --git a/sudoku-csolver/glucose.py b/sudoku-csolver/glucose.py
new file mode 100644
index 00000000..a27ed8c2
--- /dev/null
+++ b/sudoku-csolver/glucose.py
@@ -0,0 +1,63 @@
+
+cnf_in_filename = 'cnf.in'
+cnf_out_filename = 'cnf.out'
+
+import subprocess
+import re
+
+def in_file_out_file(exe_name):
+ ''' Run a minisat style solver'''
+ def solve(infilename, outfilename):
+ return subprocess.call(
+ [exe_name, infilename, outfilename]
+ )
+ return solve
+
+def in_file_out_pipe(exe_name):
+ ''' Run a precosat style solver'''
+ def solve(infilename, outfilename):
+ with open(outfilename, 'w') as fil:
+ return subprocess.call(
+ [exe_name, infilename],
+ stdout=fil
+ )
+ return solve
+
+#SAT_SOLVE = in_file_out_pipe('./lingeling')
+#SAT_SOLVE = in_file_out_file('./cryptominisat')
+SAT_SOLVE = in_file_out_file('./glucose_static')
+
+
+def print_cnf_file(clauses, fil, maxVar):
+ print >> fil, 'p cnf', maxVar , len(clauses)
+ for (i,clause) in enumerate(clauses):
+ for lit in clause:
+ print >> fil, lit,
+ print >> fil, '0'
+
+
+def get_SAT_assignments(fil):
+ assignments = []
+ for line in fil:
+ if 'UNSAT' in line.upper():
+ return None
+ for word in line.split():
+ if re.match(r'-?\d+$', word):
+ n = int(word)
+ if n == 0:
+ return assignments
+ else:
+ assignments.append(n)
+ return assignments
+
+
+def solve(clauses, maxVar):
+ assignments = []
+ with open(cnf_in_filename, 'w') as fil:
+ print_cnf_file(clauses, fil, maxVar )
+
+ SAT_SOLVE(cnf_in_filename, cnf_out_filename)
+
+ with open(cnf_out_filename, 'r') as fil:
+ assignments = get_SAT_assignments(fil)
+ return assignments
\ No newline at end of file
diff --git a/sudoku-csolver/glucose_static b/sudoku-csolver/glucose_static
new file mode 100755
index 00000000..309030bd
Binary files /dev/null and b/sudoku-csolver/glucose_static differ
diff --git a/sudoku-csolver/parse.sh b/sudoku-csolver/parse.sh
index 09d69d96..a3c5ecea 100755
--- a/sudoku-csolver/parse.sh
+++ b/sudoku-csolver/parse.sh
@@ -28,6 +28,7 @@ while IFS='' read -r line || [[ -n "$line" ]]; do
if [[ $line == $SATTIME ]]; then
number=$(echo $line|grep -Eo '[+-]?[0-9]+([.][0-9]+)?')
row+=","$number
+ timeout=1
fi
done < "$1"
diff --git a/sudoku-csolver/solved/36x36.sol b/sudoku-csolver/solved/36x36.sol
index d7a2079e..b5367862 100644
--- a/sudoku-csolver/solved/36x36.sol
+++ b/sudoku-csolver/solved/36x36.sol
@@ -1,36 +1,36 @@
-1.900000000000000000e+01 1.800000000000000000e+01 2.700000000000000000e+01 2.400000000000000000e+01 1.500000000000000000e+01 3.100000000000000000e+01 3.300000000000000000e+01 2.900000000000000000e+01 2.000000000000000000e+00 9.000000000000000000e+00 2.200000000000000000e+01 1.300000000000000000e+01 1.700000000000000000e+01 5.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 3.500000000000000000e+01 2.500000000000000000e+01 2.000000000000000000e+01 2.300000000000000000e+01 1.100000000000000000e+01 2.600000000000000000e+01 1.200000000000000000e+01 2.100000000000000000e+01 2.800000000000000000e+01 6.000000000000000000e+00 4.000000000000000000e+00 1.000000000000000000e+00 1.400000000000000000e+01 3.600000000000000000e+01 1.000000000000000000e+01 7.000000000000000000e+00 3.400000000000000000e+01 3.000000000000000000e+01 3.000000000000000000e+00 8.000000000000000000e+00
-6.000000000000000000e+00 4.000000000000000000e+00 5.000000000000000000e+00 3.400000000000000000e+01 1.200000000000000000e+01 1.000000000000000000e+00 3.200000000000000000e+01 2.800000000000000000e+01 2.300000000000000000e+01 8.000000000000000000e+00 7.000000000000000000e+00 3.100000000000000000e+01 3.000000000000000000e+00 3.300000000000000000e+01 2.700000000000000000e+01 2.200000000000000000e+01 1.000000000000000000e+01 3.000000000000000000e+01 2.400000000000000000e+01 1.900000000000000000e+01 1.800000000000000000e+01 1.600000000000000000e+01 1.300000000000000000e+01 9.000000000000000000e+00 3.500000000000000000e+01 1.700000000000000000e+01 2.600000000000000000e+01 1.500000000000000000e+01 2.100000000000000000e+01 2.000000000000000000e+01 3.600000000000000000e+01 2.900000000000000000e+01 2.500000000000000000e+01 1.100000000000000000e+01 1.400000000000000000e+01 2.000000000000000000e+00
-9.000000000000000000e+00 2.200000000000000000e+01 1.100000000000000000e+01 3.000000000000000000e+01 3.300000000000000000e+01 3.200000000000000000e+01 1.000000000000000000e+01 1.400000000000000000e+01 1.800000000000000000e+01 2.100000000000000000e+01 2.600000000000000000e+01 2.000000000000000000e+01 8.000000000000000000e+00 1.200000000000000000e+01 3.600000000000000000e+01 3.100000000000000000e+01 2.400000000000000000e+01 3.400000000000000000e+01 4.000000000000000000e+00 2.000000000000000000e+00 3.000000000000000000e+00 2.900000000000000000e+01 3.500000000000000000e+01 2.800000000000000000e+01 2.700000000000000000e+01 2.500000000000000000e+01 7.000000000000000000e+00 1.300000000000000000e+01 2.300000000000000000e+01 5.000000000000000000e+00 1.900000000000000000e+01 1.500000000000000000e+01 1.700000000000000000e+01 1.000000000000000000e+00 1.600000000000000000e+01 6.000000000000000000e+00
-3.600000000000000000e+01 3.500000000000000000e+01 2.500000000000000000e+01 2.100000000000000000e+01 2.000000000000000000e+01 2.300000000000000000e+01 1.700000000000000000e+01 1.500000000000000000e+01 2.700000000000000000e+01 1.900000000000000000e+01 1.200000000000000000e+01 1.100000000000000000e+01 9.000000000000000000e+00 4.000000000000000000e+00 1.000000000000000000e+00 1.800000000000000000e+01 6.000000000000000000e+00 1.400000000000000000e+01 2.200000000000000000e+01 5.000000000000000000e+00 3.300000000000000000e+01 3.400000000000000000e+01 7.000000000000000000e+00 1.000000000000000000e+01 2.000000000000000000e+00 3.000000000000000000e+01 3.000000000000000000e+00 1.600000000000000000e+01 2.900000000000000000e+01 8.000000000000000000e+00 1.300000000000000000e+01 3.200000000000000000e+01 2.400000000000000000e+01 2.800000000000000000e+01 3.100000000000000000e+01 2.600000000000000000e+01
-2.900000000000000000e+01 2.800000000000000000e+01 2.600000000000000000e+01 1.000000000000000000e+01 3.000000000000000000e+00 1.700000000000000000e+01 6.000000000000000000e+00 4.000000000000000000e+00 3.600000000000000000e+01 1.600000000000000000e+01 3.500000000000000000e+01 5.000000000000000000e+00 2.300000000000000000e+01 2.000000000000000000e+00 1.300000000000000000e+01 1.900000000000000000e+01 2.000000000000000000e+01 7.000000000000000000e+00 8.000000000000000000e+00 2.500000000000000000e+01 1.000000000000000000e+00 3.000000000000000000e+01 1.400000000000000000e+01 1.500000000000000000e+01 1.100000000000000000e+01 2.400000000000000000e+01 3.400000000000000000e+01 9.000000000000000000e+00 3.200000000000000000e+01 3.100000000000000000e+01 2.100000000000000000e+01 2.700000000000000000e+01 3.300000000000000000e+01 1.800000000000000000e+01 1.200000000000000000e+01 2.200000000000000000e+01
-1.600000000000000000e+01 1.300000000000000000e+01 1.400000000000000000e+01 2.000000000000000000e+00 7.000000000000000000e+00 8.000000000000000000e+00 3.400000000000000000e+01 2.400000000000000000e+01 3.000000000000000000e+00 2.500000000000000000e+01 1.000000000000000000e+00 3.000000000000000000e+01 2.800000000000000000e+01 2.100000000000000000e+01 2.900000000000000000e+01 2.600000000000000000e+01 1.100000000000000000e+01 1.500000000000000000e+01 6.000000000000000000e+00 2.700000000000000000e+01 1.700000000000000000e+01 3.600000000000000000e+01 3.100000000000000000e+01 3.200000000000000000e+01 3.300000000000000000e+01 1.000000000000000000e+01 1.800000000000000000e+01 2.200000000000000000e+01 1.900000000000000000e+01 1.200000000000000000e+01 2.000000000000000000e+01 3.500000000000000000e+01 5.000000000000000000e+00 4.000000000000000000e+00 2.300000000000000000e+01 9.000000000000000000e+00
-3.500000000000000000e+01 3.300000000000000000e+01 3.600000000000000000e+01 3.200000000000000000e+01 2.700000000000000000e+01 3.000000000000000000e+01 3.100000000000000000e+01 8.000000000000000000e+00 2.900000000000000000e+01 2.800000000000000000e+01 2.500000000000000000e+01 2.600000000000000000e+01 2.400000000000000000e+01 2.000000000000000000e+01 2.300000000000000000e+01 1.200000000000000000e+01 1.600000000000000000e+01 2.100000000000000000e+01 9.000000000000000000e+00 1.700000000000000000e+01 1.300000000000000000e+01 1.400000000000000000e+01 1.800000000000000000e+01 1.900000000000000000e+01 6.000000000000000000e+00 1.000000000000000000e+00 2.200000000000000000e+01 1.100000000000000000e+01 2.000000000000000000e+00 1.000000000000000000e+01 4.000000000000000000e+00 3.000000000000000000e+00 1.500000000000000000e+01 5.000000000000000000e+00 3.400000000000000000e+01 7.000000000000000000e+00
-1.800000000000000000e+01 3.100000000000000000e+01 1.200000000000000000e+01 7.000000000000000000e+00 2.900000000000000000e+01 2.800000000000000000e+01 3.600000000000000000e+01 3.400000000000000000e+01 3.200000000000000000e+01 2.700000000000000000e+01 3.300000000000000000e+01 2.000000000000000000e+00 1.400000000000000000e+01 1.900000000000000000e+01 3.000000000000000000e+01 9.000000000000000000e+00 2.500000000000000000e+01 1.100000000000000000e+01 1.000000000000000000e+00 2.200000000000000000e+01 1.500000000000000000e+01 2.300000000000000000e+01 2.600000000000000000e+01 5.000000000000000000e+00 4.000000000000000000e+00 3.500000000000000000e+01 1.700000000000000000e+01 2.100000000000000000e+01 2.400000000000000000e+01 3.000000000000000000e+00 8.000000000000000000e+00 2.000000000000000000e+01 6.000000000000000000e+00 1.600000000000000000e+01 1.000000000000000000e+01 1.300000000000000000e+01
-2.600000000000000000e+01 1.900000000000000000e+01 1.300000000000000000e+01 2.500000000000000000e+01 2.400000000000000000e+01 2.200000000000000000e+01 3.500000000000000000e+01 3.000000000000000000e+01 2.000000000000000000e+01 1.800000000000000000e+01 1.700000000000000000e+01 2.100000000000000000e+01 2.900000000000000000e+01 3.400000000000000000e+01 6.000000000000000000e+00 1.000000000000000000e+01 3.200000000000000000e+01 3.100000000000000000e+01 1.100000000000000000e+01 3.300000000000000000e+01 2.800000000000000000e+01 2.700000000000000000e+01 4.000000000000000000e+00 3.000000000000000000e+00 7.000000000000000000e+00 3.600000000000000000e+01 1.600000000000000000e+01 8.000000000000000000e+00 5.000000000000000000e+00 1.500000000000000000e+01 1.000000000000000000e+00 9.000000000000000000e+00 2.300000000000000000e+01 1.200000000000000000e+01 2.000000000000000000e+00 1.400000000000000000e+01
-2.300000000000000000e+01 2.100000000000000000e+01 1.500000000000000000e+01 1.600000000000000000e+01 1.700000000000000000e+01 1.400000000000000000e+01 2.400000000000000000e+01 1.200000000000000000e+01 1.900000000000000000e+01 2.200000000000000000e+01 1.300000000000000000e+01 1.000000000000000000e+01 1.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 5.000000000000000000e+00 7.000000000000000000e+00 4.000000000000000000e+00 3.600000000000000000e+01 3.200000000000000000e+01 3.500000000000000000e+01 8.000000000000000000e+00 2.900000000000000000e+01 6.000000000000000000e+00 2.600000000000000000e+01 2.700000000000000000e+01 9.000000000000000000e+00 3.400000000000000000e+01 2.000000000000000000e+01 3.300000000000000000e+01 2.800000000000000000e+01 1.100000000000000000e+01 1.800000000000000000e+01 3.100000000000000000e+01 2.500000000000000000e+01 3.000000000000000000e+01
-2.000000000000000000e+01 1.100000000000000000e+01 1.000000000000000000e+01 9.000000000000000000e+00 5.000000000000000000e+00 2.000000000000000000e+00 4.000000000000000000e+00 1.000000000000000000e+00 1.400000000000000000e+01 6.000000000000000000e+00 3.000000000000000000e+00 1.600000000000000000e+01 2.600000000000000000e+01 1.500000000000000000e+01 8.000000000000000000e+00 3.600000000000000000e+01 3.300000000000000000e+01 2.700000000000000000e+01 3.400000000000000000e+01 1.200000000000000000e+01 3.000000000000000000e+01 7.000000000000000000e+00 2.400000000000000000e+01 3.100000000000000000e+01 3.200000000000000000e+01 1.300000000000000000e+01 2.800000000000000000e+01 2.500000000000000000e+01 1.800000000000000000e+01 2.300000000000000000e+01 2.900000000000000000e+01 2.200000000000000000e+01 3.500000000000000000e+01 1.700000000000000000e+01 2.100000000000000000e+01 1.900000000000000000e+01
-4.000000000000000000e+00 6.000000000000000000e+00 1.000000000000000000e+00 8.000000000000000000e+00 3.400000000000000000e+01 3.000000000000000000e+00 2.300000000000000000e+01 1.100000000000000000e+01 1.500000000000000000e+01 7.000000000000000000e+00 5.000000000000000000e+00 9.000000000000000000e+00 3.500000000000000000e+01 2.800000000000000000e+01 2.200000000000000000e+01 1.700000000000000000e+01 1.800000000000000000e+01 1.300000000000000000e+01 2.500000000000000000e+01 2.100000000000000000e+01 2.000000000000000000e+01 1.000000000000000000e+01 1.600000000000000000e+01 2.000000000000000000e+00 3.100000000000000000e+01 2.900000000000000000e+01 1.900000000000000000e+01 1.400000000000000000e+01 1.200000000000000000e+01 3.000000000000000000e+01 3.200000000000000000e+01 3.600000000000000000e+01 2.700000000000000000e+01 2.600000000000000000e+01 3.300000000000000000e+01 2.400000000000000000e+01
-3.400000000000000000e+01 3.600000000000000000e+01 3.300000000000000000e+01 3.100000000000000000e+01 3.500000000000000000e+01 2.900000000000000000e+01 3.000000000000000000e+01 3.200000000000000000e+01 2.800000000000000000e+01 2.600000000000000000e+01 2.700000000000000000e+01 2.500000000000000000e+01 2.200000000000000000e+01 2.400000000000000000e+01 2.100000000000000000e+01 2.300000000000000000e+01 1.900000000000000000e+01 2.000000000000000000e+01 1.800000000000000000e+01 1.600000000000000000e+01 1.400000000000000000e+01 1.500000000000000000e+01 1.700000000000000000e+01 1.300000000000000000e+01 1.200000000000000000e+01 1.100000000000000000e+01 1.000000000000000000e+01 7.000000000000000000e+00 8.000000000000000000e+00 9.000000000000000000e+00 2.000000000000000000e+00 4.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00
-3.200000000000000000e+01 3.000000000000000000e+01 2.800000000000000000e+01 2.700000000000000000e+01 2.600000000000000000e+01 2.500000000000000000e+01 2.900000000000000000e+01 3.600000000000000000e+01 3.500000000000000000e+01 3.300000000000000000e+01 3.100000000000000000e+01 3.400000000000000000e+01 1.800000000000000000e+01 1.600000000000000000e+01 1.500000000000000000e+01 1.400000000000000000e+01 1.300000000000000000e+01 6.000000000000000000e+00 2.300000000000000000e+01 2.400000000000000000e+01 2.200000000000000000e+01 2.100000000000000000e+01 2.000000000000000000e+01 1.100000000000000000e+01 1.900000000000000000e+01 4.000000000000000000e+00 5.000000000000000000e+00 3.000000000000000000e+00 1.000000000000000000e+00 2.000000000000000000e+00 1.700000000000000000e+01 8.000000000000000000e+00 7.000000000000000000e+00 1.000000000000000000e+01 9.000000000000000000e+00 1.200000000000000000e+01
-2.400000000000000000e+01 2.300000000000000000e+01 2.200000000000000000e+01 2.000000000000000000e+01 1.900000000000000000e+01 1.800000000000000000e+01 2.100000000000000000e+01 1.700000000000000000e+01 1.600000000000000000e+01 1.500000000000000000e+01 1.400000000000000000e+01 1.200000000000000000e+01 1.000000000000000000e+01 3.200000000000000000e+01 9.000000000000000000e+00 3.000000000000000000e+01 8.000000000000000000e+00 5.000000000000000000e+00 7.000000000000000000e+00 6.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 2.500000000000000000e+01 3.300000000000000000e+01 3.100000000000000000e+01 2.700000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01 2.600000000000000000e+01 2.800000000000000000e+01 3.600000000000000000e+01 1.300000000000000000e+01 2.900000000000000000e+01 1.100000000000000000e+01
-2.100000000000000000e+01 1.700000000000000000e+01 1.600000000000000000e+01 1.500000000000000000e+01 1.400000000000000000e+01 1.300000000000000000e+01 2.200000000000000000e+01 2.300000000000000000e+01 1.100000000000000000e+01 2.000000000000000000e+01 1.900000000000000000e+01 1.800000000000000000e+01 7.000000000000000000e+00 1.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 1.200000000000000000e+01 5.000000000000000000e+00 3.100000000000000000e+01 1.000000000000000000e+01 9.000000000000000000e+00 3.400000000000000000e+01 8.000000000000000000e+00 2.900000000000000000e+01 3.200000000000000000e+01 3.600000000000000000e+01 6.000000000000000000e+00 2.600000000000000000e+01 2.800000000000000000e+01 3.500000000000000000e+01 2.400000000000000000e+01 3.000000000000000000e+01 3.300000000000000000e+01 2.700000000000000000e+01 2.500000000000000000e+01
-1.200000000000000000e+01 1.000000000000000000e+01 9.000000000000000000e+00 1.100000000000000000e+01 8.000000000000000000e+00 7.000000000000000000e+00 5.000000000000000000e+00 6.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 3.400000000000000000e+01 3.100000000000000000e+01 2.500000000000000000e+01 3.300000000000000000e+01 3.600000000000000000e+01 3.500000000000000000e+01 2.900000000000000000e+01 3.000000000000000000e+01 3.200000000000000000e+01 2.800000000000000000e+01 2.700000000000000000e+01 2.600000000000000000e+01 1.300000000000000000e+01 2.200000000000000000e+01 2.000000000000000000e+01 2.400000000000000000e+01 1.700000000000000000e+01 1.400000000000000000e+01 1.600000000000000000e+01 1.900000000000000000e+01 2.100000000000000000e+01 1.500000000000000000e+01 1.800000000000000000e+01 2.300000000000000000e+01
-3.000000000000000000e+00 1.000000000000000000e+00 2.000000000000000000e+00 4.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 1.300000000000000000e+01 1.000000000000000000e+01 9.000000000000000000e+00 2.400000000000000000e+01 8.000000000000000000e+00 7.000000000000000000e+00 2.700000000000000000e+01 2.600000000000000000e+01 2.800000000000000000e+01 1.100000000000000000e+01 1.700000000000000000e+01 2.900000000000000000e+01 3.500000000000000000e+01 3.600000000000000000e+01 2.500000000000000000e+01 3.300000000000000000e+01 1.900000000000000000e+01 1.200000000000000000e+01 3.000000000000000000e+01 2.300000000000000000e+01 2.100000000000000000e+01 1.800000000000000000e+01 1.500000000000000000e+01 1.600000000000000000e+01 3.400000000000000000e+01 3.100000000000000000e+01 3.200000000000000000e+01 1.400000000000000000e+01 2.200000000000000000e+01 2.000000000000000000e+01
-3.300000000000000000e+01 3.400000000000000000e+01 3.500000000000000000e+01 3.600000000000000000e+01 3.200000000000000000e+01 2.700000000000000000e+01 2.800000000000000000e+01 3.100000000000000000e+01 3.000000000000000000e+01 2.900000000000000000e+01 2.400000000000000000e+01 2.300000000000000000e+01 2.500000000000000000e+01 2.200000000000000000e+01 2.600000000000000000e+01 2.100000000000000000e+01 1.500000000000000000e+01 1.700000000000000000e+01 1.900000000000000000e+01 2.000000000000000000e+01 1.600000000000000000e+01 1.800000000000000000e+01 1.100000000000000000e+01 1.400000000000000000e+01 1.000000000000000000e+01 1.200000000000000000e+01 1.300000000000000000e+01 5.000000000000000000e+00 9.000000000000000000e+00 7.000000000000000000e+00 6.000000000000000000e+00 2.000000000000000000e+00 4.000000000000000000e+00 8.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00
-3.100000000000000000e+01 2.900000000000000000e+01 3.000000000000000000e+01 2.800000000000000000e+01 2.500000000000000000e+01 2.600000000000000000e+01 2.700000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01 3.600000000000000000e+01 3.200000000000000000e+01 3.300000000000000000e+01 2.000000000000000000e+01 2.300000000000000000e+01 2.400000000000000000e+01 1.600000000000000000e+01 1.400000000000000000e+01 1.900000000000000000e+01 2.100000000000000000e+01 1.500000000000000000e+01 9.000000000000000000e+00 1.200000000000000000e+01 1.000000000000000000e+01 2.200000000000000000e+01 1.000000000000000000e+00 2.000000000000000000e+00 8.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 1.800000000000000000e+01 1.100000000000000000e+01 7.000000000000000000e+00 1.300000000000000000e+01 1.700000000000000000e+01
-1.500000000000000000e+01 2.400000000000000000e+01 2.300000000000000000e+01 2.200000000000000000e+01 1.800000000000000000e+01 2.100000000000000000e+01 2.600000000000000000e+01 2.500000000000000000e+01 1.700000000000000000e+01 1.400000000000000000e+01 2.000000000000000000e+01 1.900000000000000000e+01 1.300000000000000000e+01 3.600000000000000000e+01 3.300000000000000000e+01 7.000000000000000000e+00 5.000000000000000000e+00 8.000000000000000000e+00 2.000000000000000000e+00 4.000000000000000000e+00 6.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 2.900000000000000000e+01 3.400000000000000000e+01 3.100000000000000000e+01 3.500000000000000000e+01 3.200000000000000000e+01 2.700000000000000000e+01 1.100000000000000000e+01 1.200000000000000000e+01 1.000000000000000000e+01 2.800000000000000000e+01 9.000000000000000000e+00 3.000000000000000000e+01 1.600000000000000000e+01
-1.700000000000000000e+01 2.000000000000000000e+01 1.900000000000000000e+01 1.200000000000000000e+01 1.600000000000000000e+01 1.100000000000000000e+01 1.800000000000000000e+01 2.200000000000000000e+01 7.000000000000000000e+00 2.000000000000000000e+00 2.100000000000000000e+01 1.500000000000000000e+01 6.000000000000000000e+00 1.000000000000000000e+01 3.000000000000000000e+00 1.000000000000000000e+00 4.000000000000000000e+00 9.000000000000000000e+00 3.100000000000000000e+01 1.300000000000000000e+01 8.000000000000000000e+00 5.000000000000000000e+00 2.800000000000000000e+01 2.400000000000000000e+01 2.300000000000000000e+01 2.600000000000000000e+01 3.000000000000000000e+01 3.300000000000000000e+01 3.600000000000000000e+01 2.500000000000000000e+01 2.700000000000000000e+01 3.400000000000000000e+01 1.400000000000000000e+01 2.900000000000000000e+01 3.200000000000000000e+01 3.500000000000000000e+01
-1.400000000000000000e+01 3.000000000000000000e+00 8.000000000000000000e+00 1.000000000000000000e+00 1.300000000000000000e+01 1.000000000000000000e+01 1.200000000000000000e+01 9.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 1.600000000000000000e+01 4.000000000000000000e+00 3.200000000000000000e+01 3.000000000000000000e+01 1.100000000000000000e+01 2.000000000000000000e+00 3.100000000000000000e+01 2.800000000000000000e+01 2.700000000000000000e+01 7.000000000000000000e+00 3.400000000000000000e+01 1.700000000000000000e+01 2.500000000000000000e+01 3.500000000000000000e+01 2.000000000000000000e+01 1.500000000000000000e+01 2.900000000000000000e+01 1.900000000000000000e+01 2.200000000000000000e+01 1.800000000000000000e+01 2.400000000000000000e+01 2.100000000000000000e+01 2.600000000000000000e+01 2.300000000000000000e+01 3.600000000000000000e+01 3.300000000000000000e+01
-7.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 2.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 1.300000000000000000e+01 1.000000000000000000e+00 1.100000000000000000e+01 1.000000000000000000e+01 8.000000000000000000e+00 1.200000000000000000e+01 2.700000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01 2.900000000000000000e+01 1.800000000000000000e+01 3.300000000000000000e+01 2.600000000000000000e+01 3.600000000000000000e+01 3.200000000000000000e+01 3.000000000000000000e+01 2.300000000000000000e+01 2.400000000000000000e+01 2.800000000000000000e+01 1.400000000000000000e+01 1.700000000000000000e+01 1.600000000000000000e+01 2.100000000000000000e+01 3.100000000000000000e+01 2.500000000000000000e+01 2.200000000000000000e+01 2.000000000000000000e+01 1.900000000000000000e+01 1.500000000000000000e+01
-3.000000000000000000e+01 2.000000000000000000e+00 3.400000000000000000e+01 3.000000000000000000e+00 1.000000000000000000e+00 9.000000000000000000e+00 8.000000000000000000e+00 3.300000000000000000e+01 3.100000000000000000e+01 1.700000000000000000e+01 3.600000000000000000e+01 3.500000000000000000e+01 2.100000000000000000e+01 2.900000000000000000e+01 3.200000000000000000e+01 2.800000000000000000e+01 2.700000000000000000e+01 2.600000000000000000e+01 1.600000000000000000e+01 1.800000000000000000e+01 2.400000000000000000e+01 2.500000000000000000e+01 2.300000000000000000e+01 2.000000000000000000e+01 5.000000000000000000e+00 1.900000000000000000e+01 1.500000000000000000e+01 1.200000000000000000e+01 1.300000000000000000e+01 2.200000000000000000e+01 7.000000000000000000e+00 1.400000000000000000e+01 1.000000000000000000e+01 6.000000000000000000e+00 1.100000000000000000e+01 4.000000000000000000e+00
-2.800000000000000000e+01 3.200000000000000000e+01 3.100000000000000000e+01 3.500000000000000000e+01 3.600000000000000000e+01 3.300000000000000000e+01 2.500000000000000000e+01 2.700000000000000000e+01 2.600000000000000000e+01 3.400000000000000000e+01 3.000000000000000000e+01 2.900000000000000000e+01 1.900000000000000000e+01 1.800000000000000000e+01 2.000000000000000000e+01 2.400000000000000000e+01 2.300000000000000000e+01 2.200000000000000000e+01 1.700000000000000000e+01 1.400000000000000000e+01 2.100000000000000000e+01 1.300000000000000000e+01 1.500000000000000000e+01 7.000000000000000000e+00 1.600000000000000000e+01 9.000000000000000000e+00 1.100000000000000000e+01 1.000000000000000000e+01 6.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 1.200000000000000000e+01 8.000000000000000000e+00 2.000000000000000000e+00 5.000000000000000000e+00 1.000000000000000000e+00
-2.700000000000000000e+01 5.000000000000000000e+00 7.000000000000000000e+00 6.000000000000000000e+00 2.300000000000000000e+01 2.400000000000000000e+01 2.000000000000000000e+00 2.100000000000000000e+01 2.200000000000000000e+01 3.200000000000000000e+01 2.800000000000000000e+01 1.400000000000000000e+01 3.600000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01 2.500000000000000000e+01 3.000000000000000000e+00 3.300000000000000000e+01 3.000000000000000000e+01 1.000000000000000000e+01 1.200000000000000000e+01 1.100000000000000000e+01 9.000000000000000000e+00 4.000000000000000000e+00 1.700000000000000000e+01 8.000000000000000000e+00 1.000000000000000000e+00 2.900000000000000000e+01 3.100000000000000000e+01 2.600000000000000000e+01 1.500000000000000000e+01 1.600000000000000000e+01 1.300000000000000000e+01 1.900000000000000000e+01 2.000000000000000000e+01 1.800000000000000000e+01
-2.500000000000000000e+01 1.600000000000000000e+01 2.900000000000000000e+01 1.900000000000000000e+01 4.000000000000000000e+00 2.000000000000000000e+01 1.500000000000000000e+01 1.800000000000000000e+01 1.300000000000000000e+01 1.200000000000000000e+01 2.300000000000000000e+01 3.000000000000000000e+00 3.100000000000000000e+01 1.100000000000000000e+01 1.400000000000000000e+01 6.000000000000000000e+00 3.000000000000000000e+01 1.000000000000000000e+01 2.600000000000000000e+01 1.000000000000000000e+00 5.000000000000000000e+00 2.200000000000000000e+01 8.000000000000000000e+00 2.700000000000000000e+01 2.100000000000000000e+01 7.000000000000000000e+00 3.200000000000000000e+01 2.000000000000000000e+00 2.800000000000000000e+01 2.400000000000000000e+01 3.300000000000000000e+01 1.700000000000000000e+01 9.000000000000000000e+00 3.600000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01
-8.000000000000000000e+00 2.600000000000000000e+01 1.800000000000000000e+01 1.700000000000000000e+01 2.200000000000000000e+01 1.200000000000000000e+01 7.000000000000000000e+00 2.000000000000000000e+01 1.000000000000000000e+01 4.000000000000000000e+00 1.100000000000000000e+01 2.400000000000000000e+01 1.500000000000000000e+01 9.000000000000000000e+00 5.000000000000000000e+00 1.300000000000000000e+01 1.000000000000000000e+00 1.600000000000000000e+01 3.200000000000000000e+01 2.900000000000000000e+01 2.000000000000000000e+00 1.900000000000000000e+01 6.000000000000000000e+00 3.400000000000000000e+01 1.400000000000000000e+01 3.000000000000000000e+00 2.500000000000000000e+01 3.600000000000000000e+01 3.300000000000000000e+01 3.500000000000000000e+01 3.000000000000000000e+01 2.300000000000000000e+01 3.100000000000000000e+01 2.700000000000000000e+01 2.800000000000000000e+01 2.100000000000000000e+01
-1.100000000000000000e+01 1.400000000000000000e+01 2.100000000000000000e+01 1.300000000000000000e+01 1.000000000000000000e+01 1.500000000000000000e+01 1.600000000000000000e+01 1.900000000000000000e+01 5.000000000000000000e+00 1.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00 4.000000000000000000e+00 1.700000000000000000e+01 7.000000000000000000e+00 8.000000000000000000e+00 1.200000000000000000e+01 2.000000000000000000e+00 2.800000000000000000e+01 3.000000000000000000e+00 3.100000000000000000e+01 3.500000000000000000e+01 3.300000000000000000e+01 3.600000000000000000e+01 1.800000000000000000e+01 3.400000000000000000e+01 2.300000000000000000e+01 2.000000000000000000e+01 3.000000000000000000e+01 2.700000000000000000e+01 2.500000000000000000e+01 2.600000000000000000e+01 2.900000000000000000e+01 2.200000000000000000e+01 2.400000000000000000e+01 3.200000000000000000e+01
-2.200000000000000000e+01 2.700000000000000000e+01 3.200000000000000000e+01 3.300000000000000000e+01 3.100000000000000000e+01 3.600000000000000000e+01 2.000000000000000000e+01 2.600000000000000000e+01 2.500000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01 2.800000000000000000e+01 3.000000000000000000e+01 1.400000000000000000e+01 1.900000000000000000e+01 2.900000000000000000e+01 2.100000000000000000e+01 3.000000000000000000e+00 1.500000000000000000e+01 1.100000000000000000e+01 7.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 1.800000000000000000e+01 8.000000000000000000e+00 1.600000000000000000e+01 1.200000000000000000e+01 2.300000000000000000e+01 4.000000000000000000e+00 1.300000000000000000e+01 9.000000000000000000e+00 1.000000000000000000e+00 2.000000000000000000e+00 2.400000000000000000e+01 1.700000000000000000e+01 1.000000000000000000e+01
-1.300000000000000000e+01 2.500000000000000000e+01 2.400000000000000000e+01 2.900000000000000000e+01 3.000000000000000000e+01 3.500000000000000000e+01 1.900000000000000000e+01 1.600000000000000000e+01 3.300000000000000000e+01 3.100000000000000000e+01 1.800000000000000000e+01 3.600000000000000000e+01 1.100000000000000000e+01 8.000000000000000000e+00 1.200000000000000000e+01 2.700000000000000000e+01 3.400000000000000000e+01 3.200000000000000000e+01 1.000000000000000000e+01 9.000000000000000000e+00 2.300000000000000000e+01 2.000000000000000000e+01 2.200000000000000000e+01 1.700000000000000000e+01 1.500000000000000000e+01 5.000000000000000000e+00 2.000000000000000000e+00 2.600000000000000000e+01 7.000000000000000000e+00 1.000000000000000000e+00 1.400000000000000000e+01 6.000000000000000000e+00 3.000000000000000000e+00 2.100000000000000000e+01 4.000000000000000000e+00 2.800000000000000000e+01
-1.000000000000000000e+01 1.500000000000000000e+01 2.000000000000000000e+01 2.600000000000000000e+01 2.800000000000000000e+01 3.400000000000000000e+01 1.400000000000000000e+01 7.000000000000000000e+00 2.400000000000000000e+01 3.000000000000000000e+01 2.900000000000000000e+01 3.200000000000000000e+01 3.300000000000000000e+01 1.300000000000000000e+01 1.800000000000000000e+01 4.000000000000000000e+00 2.200000000000000000e+01 3.600000000000000000e+01 3.000000000000000000e+00 3.500000000000000000e+01 1.900000000000000000e+01 2.000000000000000000e+00 1.000000000000000000e+00 1.600000000000000000e+01 9.000000000000000000e+00 2.100000000000000000e+01 6.000000000000000000e+00 3.100000000000000000e+01 1.100000000000000000e+01 1.700000000000000000e+01 2.300000000000000000e+01 5.000000000000000000e+00 1.200000000000000000e+01 2.500000000000000000e+01 8.000000000000000000e+00 2.700000000000000000e+01
-5.000000000000000000e+00 1.200000000000000000e+01 1.700000000000000000e+01 2.300000000000000000e+01 2.100000000000000000e+01 1.900000000000000000e+01 1.100000000000000000e+01 3.000000000000000000e+00 8.000000000000000000e+00 1.300000000000000000e+01 1.500000000000000000e+01 2.700000000000000000e+01 2.000000000000000000e+00 6.000000000000000000e+00 1.000000000000000000e+01 3.500000000000000000e+01 9.000000000000000000e+00 1.000000000000000000e+00 1.400000000000000000e+01 2.800000000000000000e+01 2.600000000000000000e+01 4.000000000000000000e+00 3.600000000000000000e+01 2.500000000000000000e+01 2.200000000000000000e+01 2.000000000000000000e+01 2.400000000000000000e+01 3.000000000000000000e+01 3.400000000000000000e+01 2.900000000000000000e+01 1.800000000000000000e+01 3.300000000000000000e+01 1.600000000000000000e+01 3.200000000000000000e+01 7.000000000000000000e+00 3.100000000000000000e+01
-2.000000000000000000e+00 7.000000000000000000e+00 3.000000000000000000e+00 1.800000000000000000e+01 9.000000000000000000e+00 6.000000000000000000e+00 1.000000000000000000e+00 5.000000000000000000e+00 2.100000000000000000e+01 2.300000000000000000e+01 4.000000000000000000e+00 2.200000000000000000e+01 1.600000000000000000e+01 2.500000000000000000e+01 1.700000000000000000e+01 1.500000000000000000e+01 2.800000000000000000e+01 2.400000000000000000e+01 1.200000000000000000e+01 8.000000000000000000e+00 2.700000000000000000e+01 3.100000000000000000e+01 3.200000000000000000e+01 3.000000000000000000e+01 3.600000000000000000e+01 1.400000000000000000e+01 3.300000000000000000e+01 3.500000000000000000e+01 1.000000000000000000e+01 1.900000000000000000e+01 1.100000000000000000e+01 1.300000000000000000e+01 2.000000000000000000e+01 3.400000000000000000e+01 2.600000000000000000e+01 2.900000000000000000e+01
-1.000000000000000000e+00 8.000000000000000000e+00 4.000000000000000000e+00 1.400000000000000000e+01 1.100000000000000000e+01 1.600000000000000000e+01 9.000000000000000000e+00 2.000000000000000000e+00 1.200000000000000000e+01 1.000000000000000000e+01 6.000000000000000000e+00 1.700000000000000000e+01 5.000000000000000000e+00 7.000000000000000000e+00 3.100000000000000000e+01 2.000000000000000000e+01 2.600000000000000000e+01 2.300000000000000000e+01 1.300000000000000000e+01 3.400000000000000000e+01 2.900000000000000000e+01 2.400000000000000000e+01 2.100000000000000000e+01 3.300000000000000000e+01 3.000000000000000000e+00 1.800000000000000000e+01 2.700000000000000000e+01 2.800000000000000000e+01 2.500000000000000000e+01 3.200000000000000000e+01 2.200000000000000000e+01 3.000000000000000000e+01 1.900000000000000000e+01 3.500000000000000000e+01 1.500000000000000000e+01 3.600000000000000000e+01
+5.000000000000000000e+00 2.700000000000000000e+01 6.000000000000000000e+00 2.000000000000000000e+00 2.100000000000000000e+01 2.200000000000000000e+01 1.900000000000000000e+01 1.400000000000000000e+01 2.900000000000000000e+01 3.200000000000000000e+01 1.100000000000000000e+01 1.500000000000000000e+01 1.700000000000000000e+01 2.500000000000000000e+01 3.000000000000000000e+00 8.000000000000000000e+00 3.300000000000000000e+01 9.000000000000000000e+00 2.400000000000000000e+01 1.600000000000000000e+01 2.800000000000000000e+01 2.000000000000000000e+01 1.000000000000000000e+01 3.600000000000000000e+01 3.500000000000000000e+01 3.000000000000000000e+01 1.200000000000000000e+01 3.100000000000000000e+01 2.300000000000000000e+01 4.000000000000000000e+00 7.000000000000000000e+00 1.000000000000000000e+00 1.800000000000000000e+01 2.600000000000000000e+01 1.300000000000000000e+01 3.400000000000000000e+01
+9.000000000000000000e+00 2.900000000000000000e+01 3.400000000000000000e+01 1.300000000000000000e+01 3.600000000000000000e+01 1.500000000000000000e+01 2.000000000000000000e+01 2.800000000000000000e+01 3.000000000000000000e+00 3.300000000000000000e+01 6.000000000000000000e+00 1.000000000000000000e+01 3.100000000000000000e+01 4.000000000000000000e+00 3.200000000000000000e+01 1.100000000000000000e+01 2.700000000000000000e+01 2.300000000000000000e+01 5.000000000000000000e+00 1.900000000000000000e+01 7.000000000000000000e+00 2.000000000000000000e+00 2.600000000000000000e+01 2.500000000000000000e+01 2.400000000000000000e+01 1.600000000000000000e+01 1.000000000000000000e+00 2.100000000000000000e+01 1.800000000000000000e+01 1.400000000000000000e+01 1.700000000000000000e+01 2.200000000000000000e+01 3.000000000000000000e+01 1.200000000000000000e+01 8.000000000000000000e+00 3.500000000000000000e+01
+3.100000000000000000e+01 4.000000000000000000e+00 2.000000000000000000e+01 1.000000000000000000e+01 2.600000000000000000e+01 3.200000000000000000e+01 1.700000000000000000e+01 2.400000000000000000e+01 1.000000000000000000e+00 1.300000000000000000e+01 3.600000000000000000e+01 2.200000000000000000e+01 1.800000000000000000e+01 2.000000000000000000e+00 1.200000000000000000e+01 3.000000000000000000e+01 1.600000000000000000e+01 2.900000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01 3.300000000000000000e+01 2.100000000000000000e+01 8.000000000000000000e+00 1.500000000000000000e+01 7.000000000000000000e+00 6.000000000000000000e+00 9.000000000000000000e+00 3.000000000000000000e+00 2.700000000000000000e+01 1.100000000000000000e+01 2.500000000000000000e+01 1.900000000000000000e+01 2.300000000000000000e+01 5.000000000000000000e+00 1.400000000000000000e+01 2.800000000000000000e+01
+1.400000000000000000e+01 3.300000000000000000e+01 7.000000000000000000e+00 2.400000000000000000e+01 1.700000000000000000e+01 1.100000000000000000e+01 9.000000000000000000e+00 1.800000000000000000e+01 1.600000000000000000e+01 8.000000000000000000e+00 5.000000000000000000e+00 1.200000000000000000e+01 2.800000000000000000e+01 2.100000000000000000e+01 3.500000000000000000e+01 3.400000000000000000e+01 2.200000000000000000e+01 1.900000000000000000e+01 2.700000000000000000e+01 4.000000000000000000e+00 3.100000000000000000e+01 3.000000000000000000e+01 1.000000000000000000e+00 2.300000000000000000e+01 3.600000000000000000e+01 2.500000000000000000e+01 2.600000000000000000e+01 2.900000000000000000e+01 1.300000000000000000e+01 3.200000000000000000e+01 6.000000000000000000e+00 2.000000000000000000e+01 1.500000000000000000e+01 1.000000000000000000e+01 3.000000000000000000e+00 2.000000000000000000e+00
+3.500000000000000000e+01 2.500000000000000000e+01 3.000000000000000000e+01 8.000000000000000000e+00 1.200000000000000000e+01 2.800000000000000000e+01 2.000000000000000000e+00 2.300000000000000000e+01 2.100000000000000000e+01 4.000000000000000000e+00 3.400000000000000000e+01 3.100000000000000000e+01 7.000000000000000000e+00 2.600000000000000000e+01 1.000000000000000000e+00 5.000000000000000000e+00 1.300000000000000000e+01 6.000000000000000000e+00 1.800000000000000000e+01 2.900000000000000000e+01 1.700000000000000000e+01 3.000000000000000000e+00 1.100000000000000000e+01 1.400000000000000000e+01 2.200000000000000000e+01 3.300000000000000000e+01 1.900000000000000000e+01 2.000000000000000000e+01 1.000000000000000000e+01 1.500000000000000000e+01 2.700000000000000000e+01 9.000000000000000000e+00 1.600000000000000000e+01 2.400000000000000000e+01 3.200000000000000000e+01 3.600000000000000000e+01
+1.900000000000000000e+01 2.300000000000000000e+01 3.000000000000000000e+00 1.800000000000000000e+01 1.000000000000000000e+00 1.600000000000000000e+01 3.000000000000000000e+01 2.500000000000000000e+01 2.700000000000000000e+01 2.600000000000000000e+01 3.500000000000000000e+01 7.000000000000000000e+00 1.500000000000000000e+01 1.400000000000000000e+01 2.400000000000000000e+01 1.000000000000000000e+01 3.600000000000000000e+01 2.000000000000000000e+01 2.200000000000000000e+01 9.000000000000000000e+00 1.300000000000000000e+01 3.200000000000000000e+01 1.200000000000000000e+01 6.000000000000000000e+00 2.000000000000000000e+00 2.800000000000000000e+01 3.400000000000000000e+01 8.000000000000000000e+00 5.000000000000000000e+00 1.700000000000000000e+01 2.900000000000000000e+01 2.100000000000000000e+01 3.100000000000000000e+01 3.300000000000000000e+01 1.100000000000000000e+01 4.000000000000000000e+00
+1.100000000000000000e+01 3.100000000000000000e+01 1.700000000000000000e+01 2.500000000000000000e+01 2.800000000000000000e+01 8.000000000000000000e+00 3.600000000000000000e+01 2.000000000000000000e+01 1.300000000000000000e+01 2.100000000000000000e+01 3.300000000000000000e+01 5.000000000000000000e+00 1.600000000000000000e+01 3.000000000000000000e+00 3.400000000000000000e+01 2.600000000000000000e+01 7.000000000000000000e+00 1.500000000000000000e+01 2.000000000000000000e+00 6.000000000000000000e+00 1.400000000000000000e+01 2.700000000000000000e+01 2.400000000000000000e+01 1.900000000000000000e+01 1.000000000000000000e+00 3.500000000000000000e+01 3.000000000000000000e+01 1.000000000000000000e+01 2.200000000000000000e+01 2.900000000000000000e+01 3.200000000000000000e+01 1.800000000000000000e+01 1.200000000000000000e+01 9.000000000000000000e+00 4.000000000000000000e+00 2.300000000000000000e+01
+2.700000000000000000e+01 2.100000000000000000e+01 4.000000000000000000e+00 2.600000000000000000e+01 2.000000000000000000e+00 7.000000000000000000e+00 1.400000000000000000e+01 1.200000000000000000e+01 3.100000000000000000e+01 1.000000000000000000e+01 3.000000000000000000e+01 1.700000000000000000e+01 2.400000000000000000e+01 2.800000000000000000e+01 9.000000000000000000e+00 1.800000000000000000e+01 1.900000000000000000e+01 1.000000000000000000e+00 2.000000000000000000e+01 3.200000000000000000e+01 2.900000000000000000e+01 5.000000000000000000e+00 3.300000000000000000e+01 3.000000000000000000e+00 2.300000000000000000e+01 3.400000000000000000e+01 6.000000000000000000e+00 2.500000000000000000e+01 1.600000000000000000e+01 3.600000000000000000e+01 1.500000000000000000e+01 3.500000000000000000e+01 1.100000000000000000e+01 8.000000000000000000e+00 2.200000000000000000e+01 1.300000000000000000e+01
+2.300000000000000000e+01 1.800000000000000000e+01 2.400000000000000000e+01 1.900000000000000000e+01 3.500000000000000000e+01 1.000000000000000000e+00 2.200000000000000000e+01 8.000000000000000000e+00 3.400000000000000000e+01 2.900000000000000000e+01 3.200000000000000000e+01 3.000000000000000000e+00 2.000000000000000000e+01 1.100000000000000000e+01 3.300000000000000000e+01 1.200000000000000000e+01 2.500000000000000000e+01 1.000000000000000000e+01 3.000000000000000000e+01 2.800000000000000000e+01 1.500000000000000000e+01 4.000000000000000000e+00 1.600000000000000000e+01 9.000000000000000000e+00 1.300000000000000000e+01 2.700000000000000000e+01 1.700000000000000000e+01 5.000000000000000000e+00 2.100000000000000000e+01 7.000000000000000000e+00 3.600000000000000000e+01 1.400000000000000000e+01 2.000000000000000000e+00 6.000000000000000000e+00 3.100000000000000000e+01 2.600000000000000000e+01
+3.200000000000000000e+01 1.200000000000000000e+01 1.000000000000000000e+01 3.600000000000000000e+01 3.300000000000000000e+01 5.000000000000000000e+00 6.000000000000000000e+00 1.900000000000000000e+01 2.800000000000000000e+01 2.300000000000000000e+01 2.700000000000000000e+01 2.500000000000000000e+01 3.500000000000000000e+01 3.000000000000000000e+01 4.000000000000000000e+00 2.100000000000000000e+01 1.400000000000000000e+01 2.200000000000000000e+01 2.600000000000000000e+01 1.000000000000000000e+00 3.400000000000000000e+01 1.300000000000000000e+01 1.800000000000000000e+01 3.100000000000000000e+01 8.000000000000000000e+00 2.000000000000000000e+00 1.100000000000000000e+01 9.000000000000000000e+00 1.500000000000000000e+01 3.000000000000000000e+00 2.000000000000000000e+01 2.400000000000000000e+01 7.000000000000000000e+00 1.600000000000000000e+01 2.900000000000000000e+01 1.700000000000000000e+01
+1.500000000000000000e+01 9.000000000000000000e+00 2.900000000000000000e+01 2.000000000000000000e+01 2.200000000000000000e+01 1.300000000000000000e+01 1.600000000000000000e+01 2.000000000000000000e+00 1.800000000000000000e+01 1.100000000000000000e+01 2.600000000000000000e+01 3.500000000000000000e+01 6.000000000000000000e+00 2.700000000000000000e+01 5.000000000000000000e+00 3.100000000000000000e+01 2.300000000000000000e+01 1.700000000000000000e+01 1.000000000000000000e+01 7.000000000000000000e+00 2.100000000000000000e+01 3.600000000000000000e+01 2.500000000000000000e+01 8.000000000000000000e+00 4.000000000000000000e+00 2.400000000000000000e+01 1.400000000000000000e+01 3.200000000000000000e+01 1.200000000000000000e+01 1.900000000000000000e+01 1.000000000000000000e+00 3.300000000000000000e+01 2.800000000000000000e+01 3.000000000000000000e+00 3.400000000000000000e+01 3.000000000000000000e+01
+3.400000000000000000e+01 3.000000000000000000e+01 1.400000000000000000e+01 3.000000000000000000e+00 1.600000000000000000e+01 6.000000000000000000e+00 4.000000000000000000e+00 1.500000000000000000e+01 9.000000000000000000e+00 7.000000000000000000e+00 2.400000000000000000e+01 1.000000000000000000e+00 8.000000000000000000e+00 3.600000000000000000e+01 1.300000000000000000e+01 2.900000000000000000e+01 2.000000000000000000e+00 3.200000000000000000e+01 1.700000000000000000e+01 2.300000000000000000e+01 1.200000000000000000e+01 1.100000000000000000e+01 2.200000000000000000e+01 3.500000000000000000e+01 2.800000000000000000e+01 3.100000000000000000e+01 1.800000000000000000e+01 2.600000000000000000e+01 3.300000000000000000e+01 2.000000000000000000e+01 1.000000000000000000e+01 2.500000000000000000e+01 5.000000000000000000e+00 2.100000000000000000e+01 2.700000000000000000e+01 1.900000000000000000e+01
+3.000000000000000000e+01 1.900000000000000000e+01 2.200000000000000000e+01 1.200000000000000000e+01 2.300000000000000000e+01 2.100000000000000000e+01 2.400000000000000000e+01 1.000000000000000000e+00 1.500000000000000000e+01 2.000000000000000000e+01 1.800000000000000000e+01 3.200000000000000000e+01 1.100000000000000000e+01 8.000000000000000000e+00 2.600000000000000000e+01 1.600000000000000000e+01 1.700000000000000000e+01 3.500000000000000000e+01 3.600000000000000000e+01 3.100000000000000000e+01 2.700000000000000000e+01 2.500000000000000000e+01 2.900000000000000000e+01 4.000000000000000000e+00 1.000000000000000000e+01 3.000000000000000000e+00 5.000000000000000000e+00 7.000000000000000000e+00 3.400000000000000000e+01 9.000000000000000000e+00 3.300000000000000000e+01 2.800000000000000000e+01 1.400000000000000000e+01 1.300000000000000000e+01 2.000000000000000000e+00 6.000000000000000000e+00
+2.000000000000000000e+00 5.000000000000000000e+00 3.600000000000000000e+01 1.000000000000000000e+00 3.200000000000000000e+01 2.000000000000000000e+01 2.300000000000000000e+01 6.000000000000000000e+00 7.000000000000000000e+00 9.000000000000000000e+00 1.700000000000000000e+01 1.400000000000000000e+01 3.300000000000000000e+01 1.800000000000000000e+01 3.100000000000000000e+01 1.500000000000000000e+01 4.000000000000000000e+00 3.000000000000000000e+00 1.300000000000000000e+01 3.000000000000000000e+01 2.400000000000000000e+01 1.900000000000000000e+01 2.800000000000000000e+01 1.100000000000000000e+01 2.700000000000000000e+01 2.200000000000000000e+01 8.000000000000000000e+00 1.600000000000000000e+01 2.900000000000000000e+01 2.500000000000000000e+01 2.100000000000000000e+01 3.400000000000000000e+01 1.000000000000000000e+01 3.500000000000000000e+01 2.600000000000000000e+01 1.200000000000000000e+01
+1.300000000000000000e+01 1.700000000000000000e+01 2.500000000000000000e+01 1.500000000000000000e+01 2.700000000000000000e+01 3.400000000000000000e+01 8.000000000000000000e+00 3.100000000000000000e+01 1.100000000000000000e+01 5.000000000000000000e+00 2.800000000000000000e+01 3.300000000000000000e+01 1.000000000000000000e+01 2.400000000000000000e+01 2.900000000000000000e+01 1.400000000000000000e+01 2.000000000000000000e+01 1.200000000000000000e+01 3.000000000000000000e+00 2.600000000000000000e+01 2.300000000000000000e+01 6.000000000000000000e+00 3.500000000000000000e+01 1.600000000000000000e+01 2.100000000000000000e+01 1.000000000000000000e+00 4.000000000000000000e+00 1.900000000000000000e+01 2.000000000000000000e+00 1.800000000000000000e+01 9.000000000000000000e+00 3.600000000000000000e+01 2.200000000000000000e+01 3.000000000000000000e+01 7.000000000000000000e+00 3.200000000000000000e+01
+7.000000000000000000e+00 2.400000000000000000e+01 1.600000000000000000e+01 6.000000000000000000e+00 3.100000000000000000e+01 1.000000000000000000e+01 3.400000000000000000e+01 2.200000000000000000e+01 3.600000000000000000e+01 3.000000000000000000e+00 1.300000000000000000e+01 3.000000000000000000e+01 9.000000000000000000e+00 1.000000000000000000e+00 2.000000000000000000e+00 2.500000000000000000e+01 5.000000000000000000e+00 2.800000000000000000e+01 8.000000000000000000e+00 1.400000000000000000e+01 1.800000000000000000e+01 3.300000000000000000e+01 1.700000000000000000e+01 2.100000000000000000e+01 1.100000000000000000e+01 2.600000000000000000e+01 3.200000000000000000e+01 3.500000000000000000e+01 2.000000000000000000e+01 1.200000000000000000e+01 1.900000000000000000e+01 2.300000000000000000e+01 4.000000000000000000e+00 2.700000000000000000e+01 1.500000000000000000e+01 2.900000000000000000e+01
+4.000000000000000000e+00 3.000000000000000000e+00 2.800000000000000000e+01 3.300000000000000000e+01 9.000000000000000000e+00 1.800000000000000000e+01 3.500000000000000000e+01 1.600000000000000000e+01 2.600000000000000000e+01 2.700000000000000000e+01 2.900000000000000000e+01 2.000000000000000000e+00 2.100000000000000000e+01 6.000000000000000000e+00 1.900000000000000000e+01 1.300000000000000000e+01 3.000000000000000000e+01 7.000000000000000000e+00 1.000000000000000000e+00 1.000000000000000000e+01 3.200000000000000000e+01 2.200000000000000000e+01 3.400000000000000000e+01 1.200000000000000000e+01 3.100000000000000000e+01 1.500000000000000000e+01 2.300000000000000000e+01 3.600000000000000000e+01 1.400000000000000000e+01 2.400000000000000000e+01 5.000000000000000000e+00 1.700000000000000000e+01 8.000000000000000000e+00 2.000000000000000000e+01 2.500000000000000000e+01 1.100000000000000000e+01
+8.000000000000000000e+00 3.500000000000000000e+01 1.100000000000000000e+01 1.400000000000000000e+01 2.900000000000000000e+01 2.600000000000000000e+01 2.100000000000000000e+01 1.000000000000000000e+01 1.200000000000000000e+01 2.500000000000000000e+01 1.900000000000000000e+01 4.000000000000000000e+00 2.200000000000000000e+01 3.200000000000000000e+01 2.700000000000000000e+01 2.300000000000000000e+01 3.400000000000000000e+01 3.600000000000000000e+01 1.500000000000000000e+01 5.000000000000000000e+00 2.000000000000000000e+00 7.000000000000000000e+00 9.000000000000000000e+00 2.000000000000000000e+01 6.000000000000000000e+00 1.300000000000000000e+01 2.800000000000000000e+01 1.700000000000000000e+01 3.000000000000000000e+01 3.300000000000000000e+01 2.400000000000000000e+01 3.100000000000000000e+01 3.000000000000000000e+00 1.000000000000000000e+00 1.600000000000000000e+01 1.800000000000000000e+01
+1.200000000000000000e+01 1.500000000000000000e+01 1.900000000000000000e+01 3.200000000000000000e+01 1.100000000000000000e+01 2.000000000000000000e+00 3.300000000000000000e+01 2.700000000000000000e+01 3.000000000000000000e+01 3.500000000000000000e+01 1.000000000000000000e+01 1.800000000000000000e+01 5.000000000000000000e+00 7.000000000000000000e+00 3.600000000000000000e+01 6.000000000000000000e+00 3.100000000000000000e+01 2.600000000000000000e+01 2.300000000000000000e+01 3.000000000000000000e+00 1.600000000000000000e+01 2.900000000000000000e+01 1.400000000000000000e+01 2.200000000000000000e+01 2.500000000000000000e+01 8.000000000000000000e+00 2.000000000000000000e+01 2.400000000000000000e+01 9.000000000000000000e+00 1.000000000000000000e+00 3.400000000000000000e+01 4.000000000000000000e+00 1.300000000000000000e+01 1.700000000000000000e+01 2.800000000000000000e+01 2.100000000000000000e+01
+3.600000000000000000e+01 1.400000000000000000e+01 8.000000000000000000e+00 3.400000000000000000e+01 2.000000000000000000e+01 2.700000000000000000e+01 1.200000000000000000e+01 3.200000000000000000e+01 2.200000000000000000e+01 2.800000000000000000e+01 2.300000000000000000e+01 2.600000000000000000e+01 3.000000000000000000e+01 1.000000000000000000e+01 1.600000000000000000e+01 4.000000000000000000e+00 3.000000000000000000e+00 3.300000000000000000e+01 2.100000000000000000e+01 2.500000000000000000e+01 9.000000000000000000e+00 1.700000000000000000e+01 1.900000000000000000e+01 2.000000000000000000e+00 2.900000000000000000e+01 1.100000000000000000e+01 3.100000000000000000e+01 1.300000000000000000e+01 6.000000000000000000e+00 5.000000000000000000e+00 3.500000000000000000e+01 1.500000000000000000e+01 2.400000000000000000e+01 1.800000000000000000e+01 1.000000000000000000e+00 7.000000000000000000e+00
+2.200000000000000000e+01 2.800000000000000000e+01 1.800000000000000000e+01 9.000000000000000000e+00 1.300000000000000000e+01 1.700000000000000000e+01 5.000000000000000000e+00 2.100000000000000000e+01 8.000000000000000000e+00 1.500000000000000000e+01 2.500000000000000000e+01 1.100000000000000000e+01 2.300000000000000000e+01 2.900000000000000000e+01 1.400000000000000000e+01 2.000000000000000000e+01 2.400000000000000000e+01 3.400000000000000000e+01 6.000000000000000000e+00 3.600000000000000000e+01 3.500000000000000000e+01 1.000000000000000000e+00 3.100000000000000000e+01 7.000000000000000000e+00 1.900000000000000000e+01 4.000000000000000000e+00 1.000000000000000000e+01 1.200000000000000000e+01 2.600000000000000000e+01 3.000000000000000000e+01 1.600000000000000000e+01 3.200000000000000000e+01 2.700000000000000000e+01 2.000000000000000000e+00 3.300000000000000000e+01 3.000000000000000000e+00
+1.000000000000000000e+00 1.600000000000000000e+01 5.000000000000000000e+00 7.000000000000000000e+00 3.000000000000000000e+01 2.400000000000000000e+01 3.000000000000000000e+00 9.000000000000000000e+00 1.900000000000000000e+01 1.400000000000000000e+01 4.000000000000000000e+00 6.000000000000000000e+00 2.000000000000000000e+00 1.700000000000000000e+01 2.500000000000000000e+01 3.500000000000000000e+01 2.100000000000000000e+01 1.800000000000000000e+01 3.200000000000000000e+01 1.300000000000000000e+01 8.000000000000000000e+00 3.400000000000000000e+01 1.500000000000000000e+01 2.600000000000000000e+01 3.300000000000000000e+01 2.300000000000000000e+01 2.200000000000000000e+01 2.800000000000000000e+01 3.600000000000000000e+01 2.700000000000000000e+01 1.100000000000000000e+01 1.200000000000000000e+01 2.000000000000000000e+01 2.900000000000000000e+01 1.000000000000000000e+01 3.100000000000000000e+01
+2.100000000000000000e+01 6.000000000000000000e+00 2.600000000000000000e+01 3.500000000000000000e+01 3.000000000000000000e+00 4.000000000000000000e+00 7.000000000000000000e+00 2.900000000000000000e+01 2.000000000000000000e+00 1.000000000000000000e+00 3.100000000000000000e+01 2.000000000000000000e+01 1.200000000000000000e+01 2.200000000000000000e+01 2.800000000000000000e+01 3.200000000000000000e+01 9.000000000000000000e+00 1.300000000000000000e+01 3.300000000000000000e+01 1.100000000000000000e+01 3.000000000000000000e+01 1.000000000000000000e+01 2.700000000000000000e+01 2.400000000000000000e+01 1.600000000000000000e+01 1.400000000000000000e+01 1.500000000000000000e+01 1.800000000000000000e+01 1.700000000000000000e+01 3.400000000000000000e+01 2.300000000000000000e+01 8.000000000000000000e+00 2.500000000000000000e+01 3.600000000000000000e+01 1.900000000000000000e+01 5.000000000000000000e+00
+3.300000000000000000e+01 1.000000000000000000e+01 2.300000000000000000e+01 2.900000000000000000e+01 2.500000000000000000e+01 3.100000000000000000e+01 1.300000000000000000e+01 3.600000000000000000e+01 1.700000000000000000e+01 3.400000000000000000e+01 1.600000000000000000e+01 2.400000000000000000e+01 2.700000000000000000e+01 1.500000000000000000e+01 8.000000000000000000e+00 1.900000000000000000e+01 1.000000000000000000e+00 1.100000000000000000e+01 1.200000000000000000e+01 2.000000000000000000e+01 5.000000000000000000e+00 1.800000000000000000e+01 4.000000000000000000e+00 2.800000000000000000e+01 3.200000000000000000e+01 7.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 3.500000000000000000e+01 2.100000000000000000e+01 2.600000000000000000e+01 3.000000000000000000e+01 9.000000000000000000e+00 2.200000000000000000e+01 6.000000000000000000e+00 1.400000000000000000e+01
+1.700000000000000000e+01 1.100000000000000000e+01 3.200000000000000000e+01 4.000000000000000000e+00 7.000000000000000000e+00 1.200000000000000000e+01 1.000000000000000000e+00 3.000000000000000000e+01 2.000000000000000000e+01 3.100000000000000000e+01 9.000000000000000000e+00 3.600000000000000000e+01 2.500000000000000000e+01 3.500000000000000000e+01 2.300000000000000000e+01 3.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 1.900000000000000000e+01 3.300000000000000000e+01 1.000000000000000000e+01 2.800000000000000000e+01 2.100000000000000000e+01 1.300000000000000000e+01 1.400000000000000000e+01 1.800000000000000000e+01 2.000000000000000000e+00 3.400000000000000000e+01 8.000000000000000000e+00 1.600000000000000000e+01 2.200000000000000000e+01 2.600000000000000000e+01 2.900000000000000000e+01 1.500000000000000000e+01 2.400000000000000000e+01 2.700000000000000000e+01
+1.000000000000000000e+01 2.000000000000000000e+00 1.300000000000000000e+01 2.700000000000000000e+01 1.500000000000000000e+01 1.900000000000000000e+01 2.600000000000000000e+01 3.000000000000000000e+00 2.400000000000000000e+01 1.700000000000000000e+01 1.400000000000000000e+01 8.000000000000000000e+00 2.900000000000000000e+01 3.300000000000000000e+01 2.000000000000000000e+01 1.000000000000000000e+00 3.200000000000000000e+01 4.000000000000000000e+00 3.100000000000000000e+01 3.500000000000000000e+01 2.200000000000000000e+01 1.600000000000000000e+01 3.000000000000000000e+01 5.000000000000000000e+00 1.200000000000000000e+01 9.000000000000000000e+00 2.100000000000000000e+01 2.300000000000000000e+01 1.100000000000000000e+01 6.000000000000000000e+00 1.800000000000000000e+01 7.000000000000000000e+00 3.400000000000000000e+01 2.800000000000000000e+01 3.600000000000000000e+01 2.500000000000000000e+01
+6.000000000000000000e+00 3.600000000000000000e+01 3.500000000000000000e+01 5.000000000000000000e+00 8.000000000000000000e+00 2.300000000000000000e+01 1.000000000000000000e+01 7.000000000000000000e+00 3.200000000000000000e+01 1.900000000000000000e+01 2.200000000000000000e+01 2.700000000000000000e+01 2.600000000000000000e+01 1.600000000000000000e+01 2.100000000000000000e+01 1.700000000000000000e+01 2.800000000000000000e+01 3.000000000000000000e+01 9.000000000000000000e+00 1.800000000000000000e+01 2.500000000000000000e+01 1.400000000000000000e+01 2.000000000000000000e+01 3.400000000000000000e+01 3.000000000000000000e+00 2.900000000000000000e+01 2.400000000000000000e+01 1.500000000000000000e+01 4.000000000000000000e+00 1.300000000000000000e+01 2.000000000000000000e+00 1.100000000000000000e+01 3.300000000000000000e+01 3.100000000000000000e+01 1.200000000000000000e+01 1.000000000000000000e+00
+2.800000000000000000e+01 2.600000000000000000e+01 3.300000000000000000e+01 2.200000000000000000e+01 1.400000000000000000e+01 3.000000000000000000e+01 2.500000000000000000e+01 1.300000000000000000e+01 4.000000000000000000e+00 1.600000000000000000e+01 2.000000000000000000e+00 2.300000000000000000e+01 3.400000000000000000e+01 9.000000000000000000e+00 7.000000000000000000e+00 2.400000000000000000e+01 1.800000000000000000e+01 2.700000000000000000e+01 1.100000000000000000e+01 1.500000000000000000e+01 3.600000000000000000e+01 1.200000000000000000e+01 3.200000000000000000e+01 2.900000000000000000e+01 2.000000000000000000e+01 5.000000000000000000e+00 3.500000000000000000e+01 1.000000000000000000e+00 3.100000000000000000e+01 1.000000000000000000e+01 3.000000000000000000e+00 6.000000000000000000e+00 2.100000000000000000e+01 1.900000000000000000e+01 1.700000000000000000e+01 8.000000000000000000e+00
+3.000000000000000000e+00 3.400000000000000000e+01 3.100000000000000000e+01 1.600000000000000000e+01 1.800000000000000000e+01 9.000000000000000000e+00 2.900000000000000000e+01 5.000000000000000000e+00 3.300000000000000000e+01 1.200000000000000000e+01 2.100000000000000000e+01 2.800000000000000000e+01 1.900000000000000000e+01 1.300000000000000000e+01 1.100000000000000000e+01 2.200000000000000000e+01 1.500000000000000000e+01 1.400000000000000000e+01 7.000000000000000000e+00 8.000000000000000000e+00 6.000000000000000000e+00 2.400000000000000000e+01 2.000000000000000000e+00 1.000000000000000000e+00 1.700000000000000000e+01 3.600000000000000000e+01 2.500000000000000000e+01 2.700000000000000000e+01 3.200000000000000000e+01 2.600000000000000000e+01 3.000000000000000000e+01 1.000000000000000000e+01 3.500000000000000000e+01 4.000000000000000000e+00 2.300000000000000000e+01 2.000000000000000000e+01
+2.900000000000000000e+01 2.000000000000000000e+01 1.000000000000000000e+00 2.100000000000000000e+01 2.400000000000000000e+01 2.500000000000000000e+01 1.100000000000000000e+01 3.500000000000000000e+01 6.000000000000000000e+00 1.800000000000000000e+01 1.500000000000000000e+01 3.400000000000000000e+01 3.600000000000000000e+01 1.200000000000000000e+01 1.000000000000000000e+01 2.000000000000000000e+00 8.000000000000000000e+00 3.100000000000000000e+01 4.000000000000000000e+00 2.700000000000000000e+01 3.000000000000000000e+00 2.600000000000000000e+01 2.300000000000000000e+01 1.700000000000000000e+01 3.000000000000000000e+01 1.900000000000000000e+01 3.300000000000000000e+01 2.200000000000000000e+01 7.000000000000000000e+00 2.800000000000000000e+01 1.300000000000000000e+01 5.000000000000000000e+00 3.200000000000000000e+01 1.400000000000000000e+01 9.000000000000000000e+00 1.600000000000000000e+01
+2.000000000000000000e+01 3.200000000000000000e+01 1.200000000000000000e+01 3.000000000000000000e+01 1.000000000000000000e+01 1.400000000000000000e+01 3.100000000000000000e+01 3.300000000000000000e+01 2.500000000000000000e+01 6.000000000000000000e+00 7.000000000000000000e+00 2.100000000000000000e+01 3.000000000000000000e+00 2.300000000000000000e+01 1.500000000000000000e+01 2.800000000000000000e+01 3.500000000000000000e+01 8.000000000000000000e+00 1.600000000000000000e+01 2.000000000000000000e+00 1.900000000000000000e+01 9.000000000000000000e+00 1.300000000000000000e+01 1.800000000000000000e+01 2.600000000000000000e+01 1.700000000000000000e+01 2.700000000000000000e+01 1.100000000000000000e+01 1.000000000000000000e+00 2.200000000000000000e+01 4.000000000000000000e+00 2.900000000000000000e+01 3.600000000000000000e+01 3.400000000000000000e+01 5.000000000000000000e+00 2.400000000000000000e+01
+1.800000000000000000e+01 8.000000000000000000e+00 9.000000000000000000e+00 1.700000000000000000e+01 1.900000000000000000e+01 3.000000000000000000e+00 2.700000000000000000e+01 4.000000000000000000e+00 1.000000000000000000e+01 2.200000000000000000e+01 1.000000000000000000e+00 1.300000000000000000e+01 1.400000000000000000e+01 3.400000000000000000e+01 6.000000000000000000e+00 7.000000000000000000e+00 1.200000000000000000e+01 2.500000000000000000e+01 2.900000000000000000e+01 2.400000000000000000e+01 1.100000000000000000e+01 2.300000000000000000e+01 3.600000000000000000e+01 3.300000000000000000e+01 5.000000000000000000e+00 2.100000000000000000e+01 1.600000000000000000e+01 3.000000000000000000e+01 2.800000000000000000e+01 3.500000000000000000e+01 3.100000000000000000e+01 2.000000000000000000e+00 2.600000000000000000e+01 3.200000000000000000e+01 2.000000000000000000e+01 1.500000000000000000e+01
+2.600000000000000000e+01 1.300000000000000000e+01 1.500000000000000000e+01 2.800000000000000000e+01 6.000000000000000000e+00 3.600000000000000000e+01 1.800000000000000000e+01 1.100000000000000000e+01 3.500000000000000000e+01 2.400000000000000000e+01 2.000000000000000000e+01 1.900000000000000000e+01 4.000000000000000000e+00 5.000000000000000000e+00 2.200000000000000000e+01 2.700000000000000000e+01 2.900000000000000000e+01 2.100000000000000000e+01 3.400000000000000000e+01 1.200000000000000000e+01 1.000000000000000000e+00 3.100000000000000000e+01 3.000000000000000000e+00 1.000000000000000000e+01 9.000000000000000000e+00 3.200000000000000000e+01 7.000000000000000000e+00 1.400000000000000000e+01 2.500000000000000000e+01 2.000000000000000000e+00 8.000000000000000000e+00 1.600000000000000000e+01 1.700000000000000000e+01 2.300000000000000000e+01 3.000000000000000000e+01 3.300000000000000000e+01
+2.400000000000000000e+01 2.200000000000000000e+01 2.700000000000000000e+01 3.100000000000000000e+01 4.000000000000000000e+00 2.900000000000000000e+01 2.800000000000000000e+01 3.400000000000000000e+01 2.300000000000000000e+01 3.000000000000000000e+01 1.200000000000000000e+01 1.600000000000000000e+01 1.000000000000000000e+00 2.000000000000000000e+01 1.700000000000000000e+01 3.300000000000000000e+01 1.100000000000000000e+01 2.000000000000000000e+00 2.500000000000000000e+01 2.100000000000000000e+01 2.600000000000000000e+01 3.500000000000000000e+01 5.000000000000000000e+00 3.200000000000000000e+01 1.500000000000000000e+01 1.000000000000000000e+01 3.600000000000000000e+01 6.000000000000000000e+00 3.000000000000000000e+00 8.000000000000000000e+00 1.400000000000000000e+01 1.300000000000000000e+01 1.900000000000000000e+01 7.000000000000000000e+00 1.800000000000000000e+01 9.000000000000000000e+00
+1.600000000000000000e+01 1.000000000000000000e+00 2.100000000000000000e+01 1.100000000000000000e+01 3.400000000000000000e+01 3.300000000000000000e+01 3.200000000000000000e+01 1.700000000000000000e+01 5.000000000000000000e+00 2.000000000000000000e+00 8.000000000000000000e+00 9.000000000000000000e+00 1.300000000000000000e+01 3.100000000000000000e+01 3.000000000000000000e+01 3.600000000000000000e+01 2.600000000000000000e+01 2.400000000000000000e+01 1.400000000000000000e+01 2.200000000000000000e+01 2.000000000000000000e+01 1.500000000000000000e+01 7.000000000000000000e+00 2.700000000000000000e+01 1.800000000000000000e+01 1.200000000000000000e+01 2.900000000000000000e+01 4.000000000000000000e+00 1.900000000000000000e+01 2.300000000000000000e+01 2.800000000000000000e+01 3.000000000000000000e+00 6.000000000000000000e+00 2.500000000000000000e+01 3.500000000000000000e+01 1.000000000000000000e+01
+2.500000000000000000e+01 7.000000000000000000e+00 2.000000000000000000e+00 2.300000000000000000e+01 5.000000000000000000e+00 3.500000000000000000e+01 1.500000000000000000e+01 2.600000000000000000e+01 1.400000000000000000e+01 3.600000000000000000e+01 3.000000000000000000e+00 2.900000000000000000e+01 3.200000000000000000e+01 1.900000000000000000e+01 1.800000000000000000e+01 9.000000000000000000e+00 1.000000000000000000e+01 1.600000000000000000e+01 2.800000000000000000e+01 1.700000000000000000e+01 4.000000000000000000e+00 8.000000000000000000e+00 6.000000000000000000e+00 3.000000000000000000e+01 3.400000000000000000e+01 2.000000000000000000e+01 1.300000000000000000e+01 3.300000000000000000e+01 2.400000000000000000e+01 3.100000000000000000e+01 1.200000000000000000e+01 2.700000000000000000e+01 1.000000000000000000e+00 1.100000000000000000e+01 2.100000000000000000e+01 2.200000000000000000e+01
diff --git a/sudoku-csolver/solved/9x9.sol b/sudoku-csolver/solved/9x9.sol
index 1a20fc53..ad71b8d6 100644
--- a/sudoku-csolver/solved/9x9.sol
+++ b/sudoku-csolver/solved/9x9.sol
@@ -1,9 +1,9 @@
+1.000000000000000000e+00 7.000000000000000000e+00 5.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 8.000000000000000000e+00 2.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00
+8.000000000000000000e+00 2.000000000000000000e+00 9.000000000000000000e+00 5.000000000000000000e+00 7.000000000000000000e+00 6.000000000000000000e+00 4.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00
+4.000000000000000000e+00 6.000000000000000000e+00 3.000000000000000000e+00 1.000000000000000000e+00 9.000000000000000000e+00 2.000000000000000000e+00 8.000000000000000000e+00 7.000000000000000000e+00 5.000000000000000000e+00
+5.000000000000000000e+00 4.000000000000000000e+00 2.000000000000000000e+00 9.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 7.000000000000000000e+00 6.000000000000000000e+00 8.000000000000000000e+00
+3.000000000000000000e+00 1.000000000000000000e+00 8.000000000000000000e+00 2.000000000000000000e+00 6.000000000000000000e+00 7.000000000000000000e+00 5.000000000000000000e+00 4.000000000000000000e+00 9.000000000000000000e+00
+7.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00 8.000000000000000000e+00 4.000000000000000000e+00 5.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00
+6.000000000000000000e+00 5.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 9.000000000000000000e+00 8.000000000000000000e+00 7.000000000000000000e+00
+2.000000000000000000e+00 3.000000000000000000e+00 1.000000000000000000e+00 7.000000000000000000e+00 8.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 4.000000000000000000e+00
9.000000000000000000e+00 8.000000000000000000e+00 7.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00
-6.000000000000000000e+00 5.000000000000000000e+00 4.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 9.000000000000000000e+00 7.000000000000000000e+00 8.000000000000000000e+00
-3.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 9.000000000000000000e+00 8.000000000000000000e+00 7.000000000000000000e+00 6.000000000000000000e+00 5.000000000000000000e+00 4.000000000000000000e+00
-8.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00 7.000000000000000000e+00 4.000000000000000000e+00 5.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00
-7.000000000000000000e+00 4.000000000000000000e+00 5.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 8.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00
-2.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 8.000000000000000000e+00 9.000000000000000000e+00 6.000000000000000000e+00 7.000000000000000000e+00 4.000000000000000000e+00 5.000000000000000000e+00
-5.000000000000000000e+00 7.000000000000000000e+00 9.000000000000000000e+00 4.000000000000000000e+00 6.000000000000000000e+00 8.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 2.000000000000000000e+00
-4.000000000000000000e+00 6.000000000000000000e+00 2.000000000000000000e+00 1.000000000000000000e+00 3.000000000000000000e+00 9.000000000000000000e+00 5.000000000000000000e+00 8.000000000000000000e+00 7.000000000000000000e+00
-1.000000000000000000e+00 3.000000000000000000e+00 8.000000000000000000e+00 5.000000000000000000e+00 7.000000000000000000e+00 2.000000000000000000e+00 4.000000000000000000e+00 6.000000000000000000e+00 9.000000000000000000e+00