Vupsen, Pupsen and 0 solution codeforces

Vupsen, Pupsen and 0 solution codeforces

Vupsen and Pupsen were gifted an integer array. Since Vupsen doesn’t like the number 00, he threw away all numbers equal to 00 from the array. As a result, he got an array aa of length nn.

Pupsen, on the contrary, likes the number 00 and he got upset when he saw the array without zeroes. To cheer Pupsen up, Vupsen decided to come up with another array bb of length nn such that ni=1aibi=0∑i=1nai⋅bi=0. Since Vupsen doesn’t like number 00the array bb must not contain numbers equal to 00. Also, the numbers in that array must not be huge, so the sum of their absolute values cannot exceed 109109. Please help Vupsen to find any such array bb!

Input

The first line contains a single integer tt (1t1001≤t≤100) — the number of test cases. The next 2t2⋅t lines contain the description of test cases. The description of each test case consists of two lines.

The first line of each test case contains a single integer nn (2n1052≤n≤105) — the length of the array.

The second line contains nn integers a1,a2,,ana1,a2,…,an (104ai104−104≤ai≤104ai0ai≠0) — the elements of the array aa.

It is guaranteed that the sum of nn over all test cases does not exceed 21052⋅105.

Output

For each test case print nn integers b1,b2,,bnb1,b2,…,bn — elements of the array bb (|b1|+|b2|++|bn|109|b1|+|b2|+…+|bn|≤109bi0bi≠0ni=1aibi=0∑i=1nai⋅bi=0).

It can be shown that the answer always exists.

Example
input

Copy
3
2
5 5
5
5 -2 10 -9 4
7
1 2 3 4 5 6 7
output

Copy
1 -1
-1 5 1 -1 -1
-10 2 2 -3 5 -1 -1
Note

In the first test case, 51+5(1)=55=05⋅1+5⋅(−1)=5−5=0. You could also print 33 3−3, for example, since 53+5(3)=1515=05⋅3+5⋅(−3)=15−15=0

In the second test case, 5(1)+(2)5+101+(9)(1)+4(1)=510+10+94=05⋅(−1)+(−2)⋅5+10⋅1+(−9)⋅(−1)+4⋅(−1)=−5−10+10+9−4=0.

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