## Avoiding Zero Problem solution Codeforces Global Round 11-

Problem statement-

A. Avoiding Zero

You are given an array of

You have to create an array of

- The array
b $b$ is a rearrangement of the arraya $a$, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets{a1,a2,…,an} $\{{a}_{1},{a}_{2},\dots ,{a}_{n}\}$ and{b1,b2,…,bn} $\{{b}_{1},{b}_{2},\dots ,{b}_{n}\}$ are equal.For example, if

a=[1,−1,0,1] $a=[1,-1,0,1]$, thenb=[−1,1,1,0] $b=[-1,1,1,0]$ andb=[0,1,−1,1] $b=[0,1,-1,1]$ are rearrangements ofa $a$, butb=[1,−1,−1,0] $b=[1,-1,-1,0]$ andb=[1,0,2,−3] $b=[1,0,2,-3]$ are not rearrangements ofa $a$. - For all
k=1,2,…,n $k=1,2,\dots ,n$ the sum of the firstk $k$ elements ofb $b$ is nonzero. Formally, for allk=1,2,…,n $k=1,2,\dots ,n$, it must holdb1+b2+⋯+bk≠0. $${b}_{1}+{b}_{2}+\cdots +{b}_{k}\ne 0\phantom{\rule{thinmathspace}{0ex}}.$$

If an array

Each test contains multiple test cases. The first line contains an integer

The first line of each testcase contains one integer

The second line of each testcase contains

For each testcase, if there is not an array

Otherwise print a line with the word YES, followed by a line with the

If there is more than one array

4 4 1 -2 3 -4 3 0 0 0 5 1 -1 1 -1 1 6 40 -31 -9 0 13 -40

YES 1 -2 3 -4 NO YES 1 1 -1 1 -1 YES -40 13 40 0 -9 -31

Explanation of the first testcase: An array with the desired properties is

- The first element of
b $b$ is1 $1$. - The sum of the first two elements of
b $b$ is−1 $-1$. - The sum of the first three elements of
b $b$ is2 $2$. - The sum of the first four elements of
b $b$ is−2 $-2$.

Explanation of the second testcase: Since all values in

Explanation of the third testcase: An array with the desired properties is

- The first element of
b $b$ is1 $1$. - The sum of the first two elements of
b $b$ is2 $2$. - The sum of the first three elements of
b $b$ is1 $1$. - The sum of the first four elements of
b $b$ is2 $2$. - The sum of the first five elements of
b $b$ is1 $1$.

Explanation of the fourth testcase: An array with the desired properties is

- The first element of
b $b$ is−40 $-40$. - The sum of the first two elements of
b $b$ is−27 $-27$. - The sum of the first three elements of
b $b$ is13 $13$. - The sum of the first four elements of
b $b$ is13 $13$. - The sum of the first five elements of
b $b$ is4 $4$. - The sum of the first six elements of
b $b$ is−27 $-27$.

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