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A. Hayato and School

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputToday Hayato came home from school with homework.

In the assignment, Hayato was given an array $$$a$$$ of length $$$n$$$. The task was to find $$$3$$$ numbers in this array whose sum is odd. At school, he claimed that there are such $$$3$$$ numbers, but Hayato was not sure, so he asked you for help.

Answer if there are such three numbers, and if so, output indices $$$i$$$, $$$j$$$, and $$$k$$$ such that $$$a_i + a_j + a_k$$$ is odd.

The odd numbers are integers that are not divisible by $$$2$$$: $$$1$$$, $$$3$$$, $$$5$$$, and so on.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

For each test case, the first line contains one integer $$$n$$$ ($$$3 \le n \le 300$$$) — the length of $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^5$$$) — the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case, in the first line print one word "YES" (without quotes) if there are $$$3$$$ numbers with an odd sum or "NO" (without quotes) if there are no such $$$3$$$ numbers.

If the answer exists, then on the second line print $$$3$$$ distinct integers $$$i, j, k$$$ ($$$1 \le i, j, k \le n$$$) — the indices of the numbers. If there are several answers, output any.

Example

Input

631 1 141 1 2 231 2 351 4 5 1 242 6 2 455 6 3 2 1

Output

YES 1 2 3 YES 3 4 1 NO YES 1 3 4 NO YES 1 3 5

Note

In the first test case, there is one way to choose $$$3$$$ numbers, and since $$$1 + 1 + 1 = 3$$$, this triple is fine for us.

In the second test case, you need to choose the numbers $$$1, 2, 2$$$, since $$$1 + 2 + 2 = 5$$$.

In the third test case, there is one way to choose three numbers, but $$$1 + 2 + 3 = 6$$$ is an even number, so the required triple does not exist.

In the fifth test case, no matter what three numbers we choose, their sum is even.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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