使用 Python 从总和值递减的集合中查找组合（没有 "of size=r"）
Find combinations (without "of size=r") from a set with decreasing sum value using Python
（为清楚起见，于 2021 年 2 月 8 日修订）
这与此处的问题类似：
Find combinations of size r from a set with decreasing sum value
这与上面 link 中发布的答案不同，因为我正在寻找没有“size r=3”的答案。
我有一组（数组）数字。
我需要将数字组合的总和从最大到最小排序，并显示数组中用于获取该行总数的数字。
数组中的任何数字每行只能使用一次，但随着总数的减少，所有数字都不必在每一行中使用。
如果不使用数字，则应使用零作为占位符，这样我就可以创建列对齐的 CSV 文件。
输入示例 #1，数组中有 7 个数字：[30,25,20,15,10,5,1]
所需的输出示例#1 格式，其中每行中的最后一个数字是该行的总和：
Beginning of list
30,25,20,15,10,5,1,106
30,25,20,15,10,5,0,105
30,25,20,15,10,0,1,101
30,25,20,15,10,0,0,100
...(all number combinations in between)
30,0,0,0,0,0,0,30
0,25,0,0,0,5,0,30
...(all number combinations in between)
0,0,0,15,0,0,1,16
0,0,0,15,0,0,0,15
0,0,0,0,10,5,0,15
0,0,0,0,10,0,1,11
0,0,0,0,0,5,1,6
0,0,0,0,0,5,0,5
0,0,0,0,0,0,1,1
End of list
此外，允许并首选显示具有相同行总计（总和）的不同组合的重复总计。
例如#1：
30,0,0,0,0,0,0,30
0,25,0,0,0,5,0,30
例如，这是基于上面输入示例 #1 的一行输出：
30,25,0,0,0,5,1,61
行中的最后一个数字是总数。总数也可以是第一个数字，但重要的是输出列表按总数降序排列。
输入示例 #2，数组中有 5 个数字：[20,15,10,5,1]
所需的输出示例#2 格式，其中每行中的最后一个数字是该行的总和：
Beginning of list
20,15,10,5,1,51
20,15,10,5,0,50
20,15,10,0,1,46
20,15,10,0,0,45
...(all number combinations in between)
20,0,10,0,0,30
0,15,10,5,0,30
...(all number combinations in between)
0,15,0,0,1,16
0,15,0,0,0,15
0,0,10,5,0,15
0,0,10,0,1,11
0,0,10,0,0,10
0,0,0,5,1,6
0,0,0,5,0,5
0,0,0,0,1,1
End of list
输入示例 #1：[30,25,20,15,10,5,1]
输出的每一行都应显示数组中的每个数字，每行最多只使用一次以获得该行的总数。
行必须按用于计算总数的数字之和降序排列。
列表中的第一个输出行将显示 30 + 25 + 20 + 15 + 10 + 5 + 1 = 106
列表中的第二个输出行将显示 30 + 25 + 20 + 15 + 10 + 5 + 0 = 105
的结果
列表中的第三个输出行将显示 30 + 25 + 20 + 15 + 10 + 0 + 1 = 101
的结果
...其余行将继续，行的总数（总和）越来越小，直到达到 1...
列表中倒数第三个输出行将显示 0 + 0 + 0 + 0 + 0 + 5 + 1 = 6
的结果
列表中倒数第二个输出行将显示 0 + 0 + 0 + 0 + 0 + 5 + 0 = 5
的结果
列表中的最后一个输出行将显示 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1
的结果
我从用户 Divyanshu 提供的代码开始，修改了不同的输入数字并将 () 添加到最后一行（但我需要使用数组中的所有数字而不是 size=4 作为此处显示):
import itertools
array = [30,25,20,15,10,5,1]
size = 4
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
for key in order:
print (key[0],answer[key[1]]) # key[0] is sum of combination
这就是我需要的输入（在此示例中）：
[30,25,20,15,10,5,1]
上面代码中的 size=4 将输出限制为数组中的 4 个数字。
如果我取出 size=4 我得到一个错误。我需要使用整个数字数组。
我可以手动将 size=4 更改为 size=1 然后 运行 然后 size=2 然后 运行 它等等。
在代码中输入 size=1 到 size=7 并 运行 对其进行操作（在此示例中为 7 次）以获取所有可能组合的列表，从而得到 7 个不同的输出。
然后我可以手动将列表放在一起，但这不适用于更大的数字集（数组）。
我可以修改上面引用的代码还是需要使用不同的方法？
我想你可以按如下方式进行：
导入以下内容：
import pandas as pd
import numpy as np
问题中代码的开头：
import itertools
array = [30,25,20,15,10,5,1]
size = 4
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
for key in order:
print (key[0],answer[key[1]]) # key[0] is sum of combination
代码，我认为可以帮助获得最终选项：
array_len = array.__len__()
# Auxiliary to place in reference to the original array
dict_array = {}
for i in range(0,array_len):
print(i)
dict_array[array[i]]=i
# Reorder the previous combinations
aux = []
for key in order:
array_zeros = np.zeros([1, array_len+1])
for i in answer[key[1]]:
print(i,dict_array[i] )
array_zeros[0][dict_array[i]] = i
# Let add the total
array_zeros[0][array_len]=key[0]
aux.append(array_zeros[0])
# Tranform into a dataframe
aux = pd.DataFrame(aux)
# This is to add the names to the columns
# for the dataframe
aux.columns=array + ['total']
aux = aux.astype(int)
print(aux.head().astype(int))
30 25 20 15 10 5 1 total
0 30 25 20 15 0 0 0 90
1 30 25 20 0 10 0 0 85
2 30 25 0 15 10 0 0 80
3 30 25 20 0 0 5 0 80
4 30 25 20 0 0 0 1 76
现在适用于所有尺寸
import itertools
import pandas as pd
import numpy as np
array = [30,25,20,15,10,5,1]
array_len = array.__len__()
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for size in range(1,array_len+1):
print(size)
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
for key in order:
print (key[0],answer[key[1]]) # key[0] is sum of combination
# Auxiliary to place in reference to the original array
dict_array = {}
for i in range(0,array_len):
print(i)
dict_array[array[i]]=i
# Reorder the previous combinations
aux = []
for key in order:
array_zeros = np.zeros([1, array_len+1])
for i in answer[key[1]]:
print(i,dict_array[i] )
array_zeros[0][dict_array[i]] = i
# Let add the total
array_zeros[0][array_len]=key[0]
aux.append(array_zeros[0])
# Tranform into a dataframe
aux = pd.DataFrame(aux)
# This is to add the names to the columns
# for the dataframe
aux.columns=array + ['total']
aux = aux.astype(int)
print(aux.head().astype(int))
30 25 20 15 10 5 1 total
0 30 25 20 15 10 5 1 106
1 30 25 20 15 10 5 0 105
2 30 25 20 15 10 0 1 101
3 30 25 20 15 10 0 0 100
4 30 25 20 15 0 5 1 96
感谢@RafaelValero (Rafael Valero)，我得以了解 pandas、numpy 和数据帧。我查找了 pandas 的选项以获得所需的输出。
这是最终代码，其中有一些额外的行供参考，但被注释掉了：
import itertools
import pandas as pd
import numpy as np
array = [30,25,20,15,10,5,1]
array_len = array.__len__()
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for size in range(1,array_len+1):
# Commented out line below as it was giving extra information
# print(size)
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
# Commented out two lines below as it was from the original code and giving extra information
#for key in order:
# print (key[0],answer[key[1]]) # key[0] is sum of combination
# Auxiliary to place in reference to the original array
dict_array = {}
for i in range(0,array_len):
# Commented out line below as it was giving extra information
# print(i)
dict_array[array[i]]=i
# Reorder the previous combinations
aux = []
for key in order:
array_zeros = np.zeros([1, array_len+1])
for i in answer[key[1]]:
# Commented out line below as it was giving extra information
# print(i,dict_array[i] )
array_zeros[0][dict_array[i]] = i
# Let add the total
array_zeros[0][array_len]=key[0]
aux.append(array_zeros[0])
# Tranform into a dataframe
aux = pd.DataFrame(aux)
# This is to add the names to the columns
# for the dataframe
# Update: removed this line below as I didn't need a header
# aux.columns=array + ['total']
aux = aux.astype(int)
# Tried option below first but it was not necessary when using to_csv
# pd.set_option('display.max_rows', None)
print(aux.to_csv(index=False,header=None))
搜索的参考资料：
类似问题：
Find combinations of size r from a set with decreasing sum value
Pandas 参考文献：
https://thispointer.com/python-pandas-how-to-display-full-dataframe-i-e-print-all-rows-columns-without-truncation/
https://pandas.pydata.org/pandas-docs/version/0.17.0/generated/pandas.DataFrame.to_csv.html
使用的在线编译器：
https://www.programiz.com/python-programming/online-compiler/
使用输入示例 #1 的输出，数组中有 7 个数字：[30,25,20,15,10,5,1]:
30,25,20,15,10,5,1,106
30,25,20,15,10,5,0,105
30,25,20,15,10,0,1,101
30,25,20,15,10,0,0,100
30,25,20,15,0,5,1,96
30,25,20,15,0,5,0,95
30,25,20,0,10,5,1,91
30,25,20,15,0,0,1,91
30,25,20,0,10,5,0,90
30,25,20,15,0,0,0,90
30,25,0,15,10,5,1,86
30,25,20,0,10,0,1,86
30,25,0,15,10,5,0,85
30,25,20,0,10,0,0,85
30,0,20,15,10,5,1,81
30,25,0,15,10,0,1,81
30,25,20,0,0,5,1,81
30,0,20,15,10,5,0,80
30,25,0,15,10,0,0,80
30,25,20,0,0,5,0,80
0,25,20,15,10,5,1,76
30,0,20,15,10,0,1,76
30,25,0,15,0,5,1,76
30,25,20,0,0,0,1,76
0,25,20,15,10,5,0,75
30,0,20,15,10,0,0,75
30,25,0,15,0,5,0,75
30,25,20,0,0,0,0,75
0,25,20,15,10,0,1,71
30,0,20,15,0,5,1,71
30,25,0,0,10,5,1,71
30,25,0,15,0,0,1,71
0,25,20,15,10,0,0,70
30,0,20,15,0,5,0,70
30,25,0,0,10,5,0,70
30,25,0,15,0,0,0,70
0,25,20,15,0,5,1,66
30,0,20,0,10,5,1,66
30,0,20,15,0,0,1,66
30,25,0,0,10,0,1,66
0,25,20,15,0,5,0,65
30,0,20,0,10,5,0,65
30,0,20,15,0,0,0,65
30,25,0,0,10,0,0,65
0,25,20,0,10,5,1,61
30,0,0,15,10,5,1,61
0,25,20,15,0,0,1,61
30,0,20,0,10,0,1,61
30,25,0,0,0,5,1,61
0,25,20,0,10,5,0,60
30,0,0,15,10,5,0,60
0,25,20,15,0,0,0,60
30,0,20,0,10,0,0,60
30,25,0,0,0,5,0,60
0,25,0,15,10,5,1,56
0,25,20,0,10,0,1,56
30,0,0,15,10,0,1,56
30,0,20,0,0,5,1,56
30,25,0,0,0,0,1,56
0,25,0,15,10,5,0,55
0,25,20,0,10,0,0,55
30,0,0,15,10,0,0,55
30,0,20,0,0,5,0,55
30,25,0,0,0,0,0,55
0,0,20,15,10,5,1,51
0,25,0,15,10,0,1,51
0,25,20,0,0,5,1,51
30,0,0,15,0,5,1,51
30,0,20,0,0,0,1,51
0,0,20,15,10,5,0,50
0,25,0,15,10,0,0,50
0,25,20,0,0,5,0,50
30,0,0,15,0,5,0,50
30,0,20,0,0,0,0,50
0,0,20,15,10,0,1,46
0,25,0,15,0,5,1,46
30,0,0,0,10,5,1,46
0,25,20,0,0,0,1,46
30,0,0,15,0,0,1,46
0,0,20,15,10,0,0,45
0,25,0,15,0,5,0,45
30,0,0,0,10,5,0,45
0,25,20,0,0,0,0,45
30,0,0,15,0,0,0,45
0,0,20,15,0,5,1,41
0,25,0,0,10,5,1,41
0,25,0,15,0,0,1,41
30,0,0,0,10,0,1,41
0,0,20,15,0,5,0,40
0,25,0,0,10,5,0,40
0,25,0,15,0,0,0,40
30,0,0,0,10,0,0,40
0,0,20,0,10,5,1,36
0,0,20,15,0,0,1,36
0,25,0,0,10,0,1,36
30,0,0,0,0,5,1,36
0,0,20,0,10,5,0,35
0,0,20,15,0,0,0,35
0,25,0,0,10,0,0,35
30,0,0,0,0,5,0,35
0,0,0,15,10,5,1,31
0,0,20,0,10,0,1,31
0,25,0,0,0,5,1,31
30,0,0,0,0,0,1,31
0,0,0,15,10,5,0,30
0,0,20,0,10,0,0,30
0,25,0,0,0,5,0,30
30,0,0,0,0,0,0,30
0,0,0,15,10,0,1,26
0,0,20,0,0,5,1,26
0,25,0,0,0,0,1,26
0,0,0,15,10,0,0,25
0,0,20,0,0,5,0,25
0,25,0,0,0,0,0,25
0,0,0,15,0,5,1,21
0,0,20,0,0,0,1,21
0,0,0,15,0,5,0,20
0,0,20,0,0,0,0,20
0,0,0,0,10,5,1,16
0,0,0,15,0,0,1,16
0,0,0,0,10,5,0,15
0,0,0,15,0,0,0,15
0,0,0,0,10,0,1,11
0,0,0,0,10,0,0,10
0,0,0,0,0,5,1,6
0,0,0,0,0,5,0,5
0,0,0,0,0,0,1,1
（为清楚起见，于 2021 年 2 月 8 日修订）
这与此处的问题类似：
Find combinations of size r from a set with decreasing sum value
这与上面 link 中发布的答案不同，因为我正在寻找没有“size r=3”的答案。
我有一组（数组）数字。
我需要将数字组合的总和从最大到最小排序，并显示数组中用于获取该行总数的数字。
数组中的任何数字每行只能使用一次，但随着总数的减少，所有数字都不必在每一行中使用。
如果不使用数字，则应使用零作为占位符，这样我就可以创建列对齐的 CSV 文件。
输入示例 #1，数组中有 7 个数字：[30,25,20,15,10,5,1]
所需的输出示例#1 格式，其中每行中的最后一个数字是该行的总和：
Beginning of list
30,25,20,15,10,5,1,106
30,25,20,15,10,5,0,105
30,25,20,15,10,0,1,101
30,25,20,15,10,0,0,100
...(all number combinations in between)
30,0,0,0,0,0,0,30
0,25,0,0,0,5,0,30
...(all number combinations in between)
0,0,0,15,0,0,1,16
0,0,0,15,0,0,0,15
0,0,0,0,10,5,0,15
0,0,0,0,10,0,1,11
0,0,0,0,0,5,1,6
0,0,0,0,0,5,0,5
0,0,0,0,0,0,1,1
End of list
此外，允许并首选显示具有相同行总计（总和）的不同组合的重复总计。 例如#1：
30,0,0,0,0,0,0,30
0,25,0,0,0,5,0,30
例如，这是基于上面输入示例 #1 的一行输出：
30,25,0,0,0,5,1,61
行中的最后一个数字是总数。总数也可以是第一个数字，但重要的是输出列表按总数降序排列。
输入示例 #2，数组中有 5 个数字：[20,15,10,5,1]
所需的输出示例#2 格式，其中每行中的最后一个数字是该行的总和：
Beginning of list
20,15,10,5,1,51
20,15,10,5,0,50
20,15,10,0,1,46
20,15,10,0,0,45
...(all number combinations in between)
20,0,10,0,0,30
0,15,10,5,0,30
...(all number combinations in between)
0,15,0,0,1,16
0,15,0,0,0,15
0,0,10,5,0,15
0,0,10,0,1,11
0,0,10,0,0,10
0,0,0,5,1,6
0,0,0,5,0,5
0,0,0,0,1,1
End of list
输入示例 #1：[30,25,20,15,10,5,1]
输出的每一行都应显示数组中的每个数字，每行最多只使用一次以获得该行的总数。 行必须按用于计算总数的数字之和降序排列。
列表中的第一个输出行将显示 30 + 25 + 20 + 15 + 10 + 5 + 1 = 106
列表中的第二个输出行将显示 30 + 25 + 20 + 15 + 10 + 5 + 0 = 105
的结果
列表中的第三个输出行将显示 30 + 25 + 20 + 15 + 10 + 0 + 1 = 101
的结果
...其余行将继续，行的总数（总和）越来越小，直到达到 1...
列表中倒数第三个输出行将显示 0 + 0 + 0 + 0 + 0 + 5 + 1 = 6
的结果
列表中倒数第二个输出行将显示 0 + 0 + 0 + 0 + 0 + 5 + 0 = 5
的结果
列表中的最后一个输出行将显示 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1
我从用户 Divyanshu 提供的代码开始，修改了不同的输入数字并将 () 添加到最后一行（但我需要使用数组中的所有数字而不是 size=4 作为此处显示):
import itertools
array = [30,25,20,15,10,5,1]
size = 4
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
for key in order:
print (key[0],answer[key[1]]) # key[0] is sum of combination
这就是我需要的输入（在此示例中）：
[30,25,20,15,10,5,1]
size=4 将输出限制为数组中的 4 个数字。 如果我取出 size=4 我得到一个错误。我需要使用整个数字数组。
我可以手动将 size=4 更改为 size=1 然后 运行 然后 size=2 然后 运行 它等等。
在代码中输入 size=1 到 size=7 并 运行 对其进行操作（在此示例中为 7 次）以获取所有可能组合的列表，从而得到 7 个不同的输出。
然后我可以手动将列表放在一起，但这不适用于更大的数字集（数组）。
我可以修改上面引用的代码还是需要使用不同的方法？
我想你可以按如下方式进行：
导入以下内容：
import pandas as pd
import numpy as np
问题中代码的开头：
import itertools
array = [30,25,20,15,10,5,1]
size = 4
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
for key in order:
print (key[0],answer[key[1]]) # key[0] is sum of combination
代码，我认为可以帮助获得最终选项：
array_len = array.__len__()
# Auxiliary to place in reference to the original array
dict_array = {}
for i in range(0,array_len):
print(i)
dict_array[array[i]]=i
# Reorder the previous combinations
aux = []
for key in order:
array_zeros = np.zeros([1, array_len+1])
for i in answer[key[1]]:
print(i,dict_array[i] )
array_zeros[0][dict_array[i]] = i
# Let add the total
array_zeros[0][array_len]=key[0]
aux.append(array_zeros[0])
# Tranform into a dataframe
aux = pd.DataFrame(aux)
# This is to add the names to the columns
# for the dataframe
aux.columns=array + ['total']
aux = aux.astype(int)
print(aux.head().astype(int))
30 25 20 15 10 5 1 total
0 30 25 20 15 0 0 0 90
1 30 25 20 0 10 0 0 85
2 30 25 0 15 10 0 0 80
3 30 25 20 0 0 5 0 80
4 30 25 20 0 0 0 1 76
现在适用于所有尺寸
import itertools
import pandas as pd
import numpy as np
array = [30,25,20,15,10,5,1]
array_len = array.__len__()
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for size in range(1,array_len+1):
print(size)
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
for key in order:
print (key[0],answer[key[1]]) # key[0] is sum of combination
# Auxiliary to place in reference to the original array
dict_array = {}
for i in range(0,array_len):
print(i)
dict_array[array[i]]=i
# Reorder the previous combinations
aux = []
for key in order:
array_zeros = np.zeros([1, array_len+1])
for i in answer[key[1]]:
print(i,dict_array[i] )
array_zeros[0][dict_array[i]] = i
# Let add the total
array_zeros[0][array_len]=key[0]
aux.append(array_zeros[0])
# Tranform into a dataframe
aux = pd.DataFrame(aux)
# This is to add the names to the columns
# for the dataframe
aux.columns=array + ['total']
aux = aux.astype(int)
print(aux.head().astype(int))
30 25 20 15 10 5 1 total
0 30 25 20 15 10 5 1 106
1 30 25 20 15 10 5 0 105
2 30 25 20 15 10 0 1 101
3 30 25 20 15 10 0 0 100
4 30 25 20 15 0 5 1 96
感谢@RafaelValero (Rafael Valero)，我得以了解 pandas、numpy 和数据帧。我查找了 pandas 的选项以获得所需的输出。
这是最终代码，其中有一些额外的行供参考，但被注释掉了：
import itertools
import pandas as pd
import numpy as np
array = [30,25,20,15,10,5,1]
array_len = array.__len__()
answer = [] # to store all combination
order = [] # to store order according to sum
number = 0 # index of combination
for size in range(1,array_len+1):
# Commented out line below as it was giving extra information
# print(size)
for comb in itertools.combinations(array,size):
answer.append(comb)
order.append([sum(comb),number]) # Storing sum and index
number += 1
order.sort(reverse=True) # sorting in decreasing order
# Commented out two lines below as it was from the original code and giving extra information
#for key in order:
# print (key[0],answer[key[1]]) # key[0] is sum of combination
# Auxiliary to place in reference to the original array
dict_array = {}
for i in range(0,array_len):
# Commented out line below as it was giving extra information
# print(i)
dict_array[array[i]]=i
# Reorder the previous combinations
aux = []
for key in order:
array_zeros = np.zeros([1, array_len+1])
for i in answer[key[1]]:
# Commented out line below as it was giving extra information
# print(i,dict_array[i] )
array_zeros[0][dict_array[i]] = i
# Let add the total
array_zeros[0][array_len]=key[0]
aux.append(array_zeros[0])
# Tranform into a dataframe
aux = pd.DataFrame(aux)
# This is to add the names to the columns
# for the dataframe
# Update: removed this line below as I didn't need a header
# aux.columns=array + ['total']
aux = aux.astype(int)
# Tried option below first but it was not necessary when using to_csv
# pd.set_option('display.max_rows', None)
print(aux.to_csv(index=False,header=None))
搜索的参考资料：
类似问题：
Find combinations of size r from a set with decreasing sum value
Pandas 参考文献：
https://thispointer.com/python-pandas-how-to-display-full-dataframe-i-e-print-all-rows-columns-without-truncation/
https://pandas.pydata.org/pandas-docs/version/0.17.0/generated/pandas.DataFrame.to_csv.html
使用的在线编译器：
https://www.programiz.com/python-programming/online-compiler/
使用输入示例 #1 的输出，数组中有 7 个数字：[30,25,20,15,10,5,1]:
30,25,20,15,10,5,1,106
30,25,20,15,10,5,0,105
30,25,20,15,10,0,1,101
30,25,20,15,10,0,0,100
30,25,20,15,0,5,1,96
30,25,20,15,0,5,0,95
30,25,20,0,10,5,1,91
30,25,20,15,0,0,1,91
30,25,20,0,10,5,0,90
30,25,20,15,0,0,0,90
30,25,0,15,10,5,1,86
30,25,20,0,10,0,1,86
30,25,0,15,10,5,0,85
30,25,20,0,10,0,0,85
30,0,20,15,10,5,1,81
30,25,0,15,10,0,1,81
30,25,20,0,0,5,1,81
30,0,20,15,10,5,0,80
30,25,0,15,10,0,0,80
30,25,20,0,0,5,0,80
0,25,20,15,10,5,1,76
30,0,20,15,10,0,1,76
30,25,0,15,0,5,1,76
30,25,20,0,0,0,1,76
0,25,20,15,10,5,0,75
30,0,20,15,10,0,0,75
30,25,0,15,0,5,0,75
30,25,20,0,0,0,0,75
0,25,20,15,10,0,1,71
30,0,20,15,0,5,1,71
30,25,0,0,10,5,1,71
30,25,0,15,0,0,1,71
0,25,20,15,10,0,0,70
30,0,20,15,0,5,0,70
30,25,0,0,10,5,0,70
30,25,0,15,0,0,0,70
0,25,20,15,0,5,1,66
30,0,20,0,10,5,1,66
30,0,20,15,0,0,1,66
30,25,0,0,10,0,1,66
0,25,20,15,0,5,0,65
30,0,20,0,10,5,0,65
30,0,20,15,0,0,0,65
30,25,0,0,10,0,0,65
0,25,20,0,10,5,1,61
30,0,0,15,10,5,1,61
0,25,20,15,0,0,1,61
30,0,20,0,10,0,1,61
30,25,0,0,0,5,1,61
0,25,20,0,10,5,0,60
30,0,0,15,10,5,0,60
0,25,20,15,0,0,0,60
30,0,20,0,10,0,0,60
30,25,0,0,0,5,0,60
0,25,0,15,10,5,1,56
0,25,20,0,10,0,1,56
30,0,0,15,10,0,1,56
30,0,20,0,0,5,1,56
30,25,0,0,0,0,1,56
0,25,0,15,10,5,0,55
0,25,20,0,10,0,0,55
30,0,0,15,10,0,0,55
30,0,20,0,0,5,0,55
30,25,0,0,0,0,0,55
0,0,20,15,10,5,1,51
0,25,0,15,10,0,1,51
0,25,20,0,0,5,1,51
30,0,0,15,0,5,1,51
30,0,20,0,0,0,1,51
0,0,20,15,10,5,0,50
0,25,0,15,10,0,0,50
0,25,20,0,0,5,0,50
30,0,0,15,0,5,0,50
30,0,20,0,0,0,0,50
0,0,20,15,10,0,1,46
0,25,0,15,0,5,1,46
30,0,0,0,10,5,1,46
0,25,20,0,0,0,1,46
30,0,0,15,0,0,1,46
0,0,20,15,10,0,0,45
0,25,0,15,0,5,0,45
30,0,0,0,10,5,0,45
0,25,20,0,0,0,0,45
30,0,0,15,0,0,0,45
0,0,20,15,0,5,1,41
0,25,0,0,10,5,1,41
0,25,0,15,0,0,1,41
30,0,0,0,10,0,1,41
0,0,20,15,0,5,0,40
0,25,0,0,10,5,0,40
0,25,0,15,0,0,0,40
30,0,0,0,10,0,0,40
0,0,20,0,10,5,1,36
0,0,20,15,0,0,1,36
0,25,0,0,10,0,1,36
30,0,0,0,0,5,1,36
0,0,20,0,10,5,0,35
0,0,20,15,0,0,0,35
0,25,0,0,10,0,0,35
30,0,0,0,0,5,0,35
0,0,0,15,10,5,1,31
0,0,20,0,10,0,1,31
0,25,0,0,0,5,1,31
30,0,0,0,0,0,1,31
0,0,0,15,10,5,0,30
0,0,20,0,10,0,0,30
0,25,0,0,0,5,0,30
30,0,0,0,0,0,0,30
0,0,0,15,10,0,1,26
0,0,20,0,0,5,1,26
0,25,0,0,0,0,1,26
0,0,0,15,10,0,0,25
0,0,20,0,0,5,0,25
0,25,0,0,0,0,0,25
0,0,0,15,0,5,1,21
0,0,20,0,0,0,1,21
0,0,0,15,0,5,0,20
0,0,20,0,0,0,0,20
0,0,0,0,10,5,1,16
0,0,0,15,0,0,1,16
0,0,0,0,10,5,0,15
0,0,0,15,0,0,0,15
0,0,0,0,10,0,1,11
0,0,0,0,10,0,0,10
0,0,0,0,0,5,1,6
0,0,0,0,0,5,0,5
0,0,0,0,0,0,1,1