# Geometric Mean Inequality Codechef Solution | APRIL CHALLENGE

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Geometric Mean Inequality Codechef Solution

You are given an array AA of length NN containing the elements −1−1 and 11 only. Determine if it is possible to rearrange the array AA in such a way that AiAi is not the geometric mean of Ai−1Ai−1 and Ai+1Ai+1, for all ii such that 2≤i≤N−12≤i≤N−1.

YY is said to be the geometric mean of XX and ZZ if Y2=X⋅ZY2=X⋅Z.

### Input Format

• The first line contains a single integer TT – the number of test cases. Then the test cases follow.
• The first line of each test case contains an integer NN – the size of the array AA.
• The second line of each test case contains NN space-separated integers A1,A2,…,ANA1,A2,…,AN denoting the array AA.

### Output Format

For each test case, output `Yes` if it is possible to rearrange AA in such a way that AiAi is not the geometric mean of Ai−1Ai−1 and Ai+1Ai+1, where 2≤i≤N−12≤i≤N−1. Otherwise output `No`.

You may print each character of `Yes` and `No` in uppercase or lowercase (for example, `yes``yEs``YES` will be considered identical).

### Constraints

• 1≤T≤2001≤T≤200
• 3≤N≤10003≤N≤1000
• Ai∈{−1,1}Ai∈{−1,1}

### Sample Input 1

``````3
5
1 1 1 -1 -1
3
1 1 1
6
1 -1 -1 -1 -1 1
``````

### Sample Output 1

``````Yes
No
Yes
``````

### Explanation

Test case 1: We can rearrange the array AA to [1,1,−1,−1,1][1,1,−1,−1,1]. One can see that Ai≠Ai−1⋅Ai+1Ai≠Ai−1⋅Ai+1, for any 2≤i≤N−12≤i≤N−1.

Test case 2: None of the rearrangements of AA satisy the given condition.