A. Ideal Generator

Felven2025-04-27 20:48

time limit per test

1 second

memory limit per test

256 megabytes

We call an array aa, consisting of kk positive integers, palindromic if [a1,a2,...,ak]=[ak,ak−1,...,a1][a1,a2,...,ak]=[ak,ak−1,...,a1]. For example, the arrays [1,2,1][1,2,1] and [5,1,1,5][5,1,1,5] are palindromic, while the arrays [1,2,3][1,2,3] and [21,12][21,12] are not.

We call a number kk an ideal generator if any integer nn (n≥kn≥k) can be represented as the sum of the elements of a palindromic array of length exactly kk. Each element of the array must be greater than 00.

For example, the number 11 is an ideal generator because any natural number nn can be generated using the array [n][n]. However, the number 22 is not an ideal generator --- there is no palindromic array of length 22 that sums to 33.

Determine whether the given number kk is an ideal generator.

Input

The first line of the input contains one integer tt (1≤t≤10001≤t≤1000) --- the number of test cases.

The first and only line of each test case contains one integer kk (1≤k≤10001≤k≤1000).

Output

For each number kk, you need to output the word "YES" if it is an ideal generator, or "NO" otherwise.

You may output "Yes" and "No" in any case (for example, the strings "yES", "yes", and "Yes" will be recognized as a positive answer).

Example

Input

Copy

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1000

Output

Copy

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YES
NO
YES
YES
NO

解题说明：此题是一道数学题，找规律能发现，k为偶数时无法找到这样的回文数列，只有奇数可以。

cpp 复制代码

#include <bits/stdc++.h>
using namespace std;

int main() {
	int t;
	cin >> t;
	while (t--)
	{
		int n;
		cin >> n;
		if (n % 2 == 1)
		{
			cout << "YES" << endl;
		}
		else
		{
			cout << "NO" << endl;
		}
	}
	return 0;
}