Pairsumonious Numbers

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Skyming  like  some games with numbers very much .One day he meet a problem .

For 10 > N > 2 numbers we form N*(N-1)/2 sums by adding every pair of the numbers. Your task is to find the N numbers given the sums. Each line of input contains N followed by N*(N-1)/2 integer numbers separated by a space. 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". Can you help him? ^_^

Input

The input contains several test cases, each test case consisting of two lines. The first line of each test case contains the number N(10 > N > 2 ). The second line followed by N*(N-1)/2 integer numbers separated by a space. Process to end of file.

Output

Your task is to find the N numbers given the sums.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