human
Can you solve the below in PYTHON3?
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...

Give me a 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?
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()