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Problem 1053. -- Pairsumonious Numbers

Pairsumonious Numbers

Time Limit: 1 Sec  Memory Limit: 64 MB
Submit: 5  Solved: 0
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Description

Any set of n integers form n(n - 1)/2 sums by adding every possible pair. Your task is to find the n integers given the set of sums.

Input

Each line of input contains n followed by n(n - 1)/2 integer numbers separated by a space, where 2 < n < 10.

Output

For each line of input, output one line containing n integers in non-descending order such that the input numbers are pairwise sums of the n numbers. If there is more than one solution, any one will do. If there is no solution, print ``Impossible"...

Sample Input

3 1269 1160 1663
3 1 1 1
5 226 223 225 224 227 229 228 226 225 227
5 216 210 204 212 220 214 222 208 216 210
5 -1 0 -1 -2 1 0 -1 1 0 -1
5 79950 79936 79942 79962 79954 79972 79960 79968 79924 79932

Sample Output

383 777 886
Impossible
111 112 113 114 115
101 103 107 109 113
-1 -1 0 0 1
39953 39971 39979 39983 39989

HINT

poj2466

Source

Waterloo local 2001.09.29

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