A. Hayato and School
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Today 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.