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Avoiding Zero Problem solution Codeforces Global Round 11

Avoiding Zero Problem solution Codeforces Global Round 11-

This Problem is taken from codeforces global round 11. This is a very simple problem and strongly recommended to try this problem yourself before jumping to a solution directly.


Problem statement-


 A. Avoiding Zero

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array of n integers a1,a2,,an.

You have to create an array of n integers b1,b2,,bn such that:

  • The array b is a rearrangement of the array 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} and {b1,b2,,bn} are equal.

    For example, if a=[1,1,0,1], then b=[1,1,1,0] and b=[0,1,1,1] are rearrangements of a, but b=[1,1,1,0] and b=[1,0,2,3] are not rearrangements of a.

  • For all k=1,2,,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,,n, it must hold
    b1+b2++bk0.

If an array b1,b2,,bn with the required properties does not exist, you have to print NO.

Input

Each test contains multiple test cases. The first line contains an integer t (1t1000) — the number of test cases. The description of the test cases follows.

The first line of each testcase contains one integer n (1n50)  — the length of the array a.

The second line of each testcase contains n integers a1,a2,,an (50ai50)  — the elements of a.

Output

For each testcase, if there is not an array b1,b2,,bn with the required properties, print a single line with the word NO.

Otherwise print a line with the word YES, followed by a line with the n integers b1,b2,,bn.

If there is more than one array b1,b2,,bn satisfying the required properties, you can print any of them.

Example
input
Copy
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
output
Copy
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note

Explanation of the first testcase: An array with the desired properties is b=[1,2,3,4]. For this array, it holds:

  • The first element of b is 1.
  • The sum of the first two elements of b is 1.
  • The sum of the first three elements of b is 2.
  • The sum of the first four elements of b is 2.

Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b1=0). Hence in this case the answer is NO.

Explanation of the third testcase: An array with the desired properties is b=[1,1,1,1,1]. For this array, it holds:

  • The first element of b is 1.
  • The sum of the first two elements of b is 2.
  • The sum of the first three elements of b is 1.
  • The sum of the first four elements of b is 2.
  • The sum of the first five elements of b is 1.

Explanation of the fourth testcase: An array with the desired properties is b=[40,13,40,0,9,31]. For this array, it holds:

  • The first element of b is 40.
  • The sum of the first two elements of b is 27.
  • The sum of the first three elements of b is 13.
  • The sum of the first four elements of b is 13.
  • The sum of the first five elements of b is 4.
  • The sum of the first six elements of b is 27.
Avoiding Zero Problem solution Codeforces Global Round 11



Solution-

According to the problem, it is not possible to make array B  if sum of all elements of array A is zero.
so if the sum of all elements of the array A is is zero we will simply print NO otherwise we will pint Yes.
Now our task is to print array B too. so we have two choices now either sum of all elements of array A is greater than 0 or less than 0. 
if sum >0 we will print array A in non-increasing order because in this case sum of element b at any point can not equal to 0. else we print array A in increasing order.
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Complete code of this Problem-


 


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