#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1);
const long long mod = 998244353;
const double eps = 1e-10;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int n, m;
int a[200005], s[2], st[200005], tp, sum[200005];
int main() {
  int t = read();
  while (t--) {
    n = read();
    s[0] = s[1] = 0;
    for (int i = 1; i <= n; i++) a[i] = read(), s[a[i]]++;
    if (!s[0]) {
      puts("NO");
      continue;
    }
    if (s[1] & 1) {
      puts("NO");
      continue;
    }
    if (!s[1]) {
      puts("YES");
      puts("0");
    } else {
      tp = 0;
      int w = 0;
      for (int i = 1; i <= n; i++) {
        sum[i] = sum[i - 1] + a[i];
        if (a[i] == 0 && sum[i - 1] % 2 == 0 && (s[1] - sum[i - 1]) % 2 == 0) {
          w = i;
          break;
        }
      }
      if (!w) {
        int len = 0, LL = 0;
        for (int i = 1; i <= n && !w; i++) {
          if (a[i] == 0)
            len++;
          else {
            if (len & 1) w = i - 1, LL = len;
            len = 0;
          }
        }
        if (!w)
          puts("NO");
        else {
          for (int i = w - LL; i <= w - 3; i += 2) {
            st[++tp] = i;
            a[i + 1] = a[i + 2] = 1;
          }
          st[++tp] = w - 1;
          a[w - 1] = a[w + 1] = 0;
          puts("YES");
          for (int i = w; i <= n - 2; i++) {
            if (a[i] == 0) {
              if (a[i + 1] == 0) continue;
              if (a[i + 2] == 1) {
                st[++tp] = i;
                a[i + 1] = a[i + 2] = 0;
                continue;
              }
              if (a[i + 3] == 1) {
                st[++tp] = i + 1;
                a[i + 1] = a[i + 3] = 0;
                continue;
              }
              st[++tp] = i + 1;
              st[++tp] = i;
              a[i + 1] = a[i + 2] = 0, a[i + 3] = 1;
            }
          }
          for (int i = w; i >= 3; i--) {
            if (a[i] == 0) {
              if (a[i - 1] == 0) continue;
              if (a[i - 2] == 1) {
                st[++tp] = i - 2;
                a[i - 1] = a[i - 2] = 0;
                continue;
              }
              if (a[i - 3] == 1) {
                st[++tp] = i - 3;
                a[i - 1] = a[i - 3] = 0;
                continue;
              }
              st[++tp] = i - 3;
              st[++tp] = i - 2;
              a[i - 1] = a[i - 2] = 0, a[i - 3] = 1;
            }
          }
          printf("%d\n", tp);
          for (int i = 1; i <= tp; i++) printf("%d ", st[i]);
          puts("");
        }
      } else {
        puts("YES");
        for (int i = w; i <= n - 2; i++) {
          if (a[i] == 0) {
            if (a[i + 1] == 0) continue;
            if (a[i + 2] == 1) {
              st[++tp] = i;
              a[i + 1] = a[i + 2] = 0;
              continue;
            }
            if (a[i + 3] == 1) {
              st[++tp] = i + 1;
              a[i + 1] = a[i + 3] = 0;
              continue;
            }
            st[++tp] = i + 1;
            st[++tp] = i;
            a[i + 1] = a[i + 2] = 0, a[i + 3] = 1;
          }
        }
        for (int i = w; i >= 3; i--) {
          if (a[i] == 0) {
            if (a[i - 1] == 0) continue;
            if (a[i - 2] == 1) {
              st[++tp] = i - 2;
              a[i - 1] = a[i - 2] = 0;
              continue;
            }
            if (a[i - 3] == 1) {
              st[++tp] = i - 3;
              a[i - 1] = a[i - 3] = 0;
              continue;
            }
            st[++tp] = i - 3;
            st[++tp] = i - 2;
            a[i - 1] = a[i - 2] = 0, a[i - 3] = 1;
          }
        }
        printf("%d\n", tp);
        for (int i = 1; i <= tp; i++) printf("%d ", st[i]);
        puts("");
      }
    }
  }
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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 of a we will get [1, 1, 1, 1], which cannot be transformed to [0, 0, 0, 0].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1);
const long long mod = 998244353;
const double eps = 1e-10;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int n, m;
int a[200005], s[2], st[200005], tp, sum[200005];
int main() {
  int t = read();
  while (t--) {
    n = read();
    s[0] = s[1] = 0;
    for (int i = 1; i <= n; i++) a[i] = read(), s[a[i]]++;
    if (!s[0]) {
      puts("NO");
      continue;
    }
    if (s[1] & 1) {
      puts("NO");
      continue;
    }
    if (!s[1]) {
      puts("YES");
      puts("0");
    } else {
      tp = 0;
      int w = 0;
      for (int i = 1; i <= n; i++) {
        sum[i] = sum[i - 1] + a[i];
        if (a[i] == 0 && sum[i - 1] % 2 == 0 && (s[1] - sum[i - 1]) % 2 == 0) {
          w = i;
          break;
        }
      }
      if (!w) {
        int len = 0, LL = 0;
        for (int i = 1; i <= n && !w; i++) {
          if (a[i] == 0)
            len++;
          else {
            if (len & 1) w = i - 1, LL = len;
            len = 0;
          }
        }
        if (!w)
          puts("NO");
        else {
          for (int i = w - LL; i <= w - 3; i += 2) {
            st[++tp] = i;
            a[i + 1] = a[i + 2] = 1;
          }
          st[++tp] = w - 1;
          a[w - 1] = a[w + 1] = 0;
          puts("YES");
          for (int i = w; i <= n - 2; i++) {
            if (a[i] == 0) {
              if (a[i + 1] == 0) continue;
              if (a[i + 2] == 1) {
                st[++tp] = i;
                a[i + 1] = a[i + 2] = 0;
                continue;
              }
              if (a[i + 3] == 1) {
                st[++tp] = i + 1;
                a[i + 1] = a[i + 3] = 0;
                continue;
              }
              st[++tp] = i + 1;
              st[++tp] = i;
              a[i + 1] = a[i + 2] = 0, a[i + 3] = 1;
            }
          }
          for (int i = w; i >= 3; i--) {
            if (a[i] == 0) {
              if (a[i - 1] == 0) continue;
              if (a[i - 2] == 1) {
                st[++tp] = i - 2;
                a[i - 1] = a[i - 2] = 0;
                continue;
              }
              if (a[i - 3] == 1) {
                st[++tp] = i - 3;
                a[i - 1] = a[i - 3] = 0;
                continue;
              }
              st[++tp] = i - 3;
              st[++tp] = i - 2;
              a[i - 1] = a[i - 2] = 0, a[i - 3] = 1;
            }
          }
          printf("%d\n", tp);
          for (int i = 1; i <= tp; i++) printf("%d ", st[i]);
          puts("");
        }
      } else {
        puts("YES");
        for (int i = w; i <= n - 2; i++) {
          if (a[i] == 0) {
            if (a[i + 1] == 0) continue;
            if (a[i + 2] == 1) {
              st[++tp] = i;
              a[i + 1] = a[i + 2] = 0;
              continue;
            }
            if (a[i + 3] == 1) {
              st[++tp] = i + 1;
              a[i + 1] = a[i + 3] = 0;
              continue;
            }
            st[++tp] = i + 1;
            st[++tp] = i;
            a[i + 1] = a[i + 2] = 0, a[i + 3] = 1;
          }
        }
        for (int i = w; i >= 3; i--) {
          if (a[i] == 0) {
            if (a[i - 1] == 0) continue;
            if (a[i - 2] == 1) {
              st[++tp] = i - 2;
              a[i - 1] = a[i - 2] = 0;
              continue;
            }
            if (a[i - 3] == 1) {
              st[++tp] = i - 3;
              a[i - 1] = a[i - 3] = 0;
              continue;
            }
            st[++tp] = i - 3;
            st[++tp] = i - 2;
            a[i - 1] = a[i - 2] = 0, a[i - 3] = 1;
          }
        }
        printf("%d\n", tp);
        for (int i = 1; i <= tp; i++) printf("%d ", st[i]);
        puts("");
      }
    }
  }
  return 0;
}

```