human
You are given a sequence a of length n consisting of 0s and 1s.

You can perform the following operation on this sequence: 

  * Pick an index i from 1 to n-2 (inclusive). 
  * Change all of a_{i}, a_{i+1}, a_{i+2} to a_{i} ⊕ a_{i+1} ⊕ a_{i+2} simultaneously, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR)

Find a sequence of at most n operations that changes all elements of a to 0s or report that it's impossible.

We can prove that if there exists a sequence of operations of any length that changes all elements of a to 0s, then there is also such a sequence of length not greater than n.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4).

The first line of each test case contains a single integer n (3 ≤ n ≤ 2⋅10^5) — the length of a.

The second line of each test case contains n integers a_1, a_2, …, a_n (a_i = 0 or a_i = 1) — elements of a.

It is guaranteed that the sum of n over all test cases does not exceed 2⋅10^5.

Output

For each test case, do the following: 

  * if there is no way of making all the elements of a equal to 0 after performing the above operation some number of times, print "NO". 
  * otherwise, in the first line print "YES", in the second line print k (0 ≤ k ≤ n) — the number of operations that you want to perform on a, and in the third line print a sequence b_1, b_2, ..., b_k (1 ≤ b_i ≤ n - 2) — the indices on which the operation should be applied. 


If there are multiple solutions, you may print any.

Example

Input

3
3
0 0 0
5
1 1 1 1 0
4
1 0 0 1

Output

YES
0
YES
2
3 1
NO

Note

In the first example, the sequence contains only 0s so we don't need to change anything.

In the second example, we can transform [1, 1, 1, 1, 0] to [1, 1, 0, 0, 0] and then to [0, 0, 0, 0, 0] by performing the operation on the third element of a and then on the first element of a.

In the third example, no matter whether we first perform the operation on the first or on the second element...
Using python3 can you solve the prior task?
assistant
#Here is Python code to find a sequence of at most n operations that changes all elements of a to 0s or report that it's impossible.

import collections
import math
import itertools
import  sys
import time
import random

def fast_input():
    return sys.stdin.readline().strip()

input = fast_input

def ints_input():
    return list(int(x) for x in input().split())

def int_input():
    return int(input())

def solve():
    n = int_input()
    a = ints_input()
    if sum(a) % 2 == 1:
        print('NO')
        return
    reversed = False
    ops = []
    def do_op(i):
        ops.append(i+1)
        a[i] = a[i+1] = a[i+2] = a[i] ^ a[i+1] ^ a[i+2]
    if a[0] == 1:
        i = 1
        found = False
        while i+1 < n:
            if a[i] == a[i+1]:
                i += 2
            else:
                found = True
                break
        if not found:
            if i == n-1 and a[i] == 1:
                print('NO')
                return
            else:
                reversed = True
                a = a[::-1]
                if a[0] == 1:
                    do_op(0)
        else:
            x = i
            while x >= 1:
                do_op(x-1)
                x -= 2
    p = 1
    while p+1 < n:
        if a[p] != a[p+1]:
            do_op(p)
            if a[p] == 0:
                p += 2
        else:
            if a[p] != 0:
                do_op(p-1)
            p += 2
    print('YES')
    print(len(ops))
    if reversed:
        ops = [n-1-i for i in ops]
    print(' '.join([str(x) for x in ops]))





if True:
    for _ in range(int_input()):
        solve()
else:
    solve()