#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
using namespace std;
template <class T>
using rque = priority_queue<T, vector<T>, greater<T>>;
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (b > a) {
    a = b;
    return 1;
  }
  return 0;
}
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  if (b == 0) return a;
  long long cnt = a % b;
  while (cnt != 0) {
    a = b;
    b = cnt;
    cnt = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
struct UnionFind {
  vector<long long> data;
  int num;
  UnionFind(int sz) {
    data.assign(sz, -1);
    num = sz;
  }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    num--;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  long long size(int k) { return (-data[find(k)]); }
  bool same(int x, int y) { return find(x) == find(y); }
};
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
long long mpow2(long long x, long long n, long long mod) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
constexpr int mod = 1000000007;
using mint = ModInt<mod>;
mint mpow(mint x, long long n) {
  mint ans = 1;
  while (n != 0) {
    if (n & 1) ans *= x;
    x *= x;
    n = n >> 1;
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  cout << fixed << setprecision(15);
  int T;
  cin >> T;
  while (T--) {
    long long n;
    cin >> n;
    long long a[n];
    for (long long i = 0; i < (n); i++) cin >> a[i];
    vector<long long> ans;
    int f = 0, o = 0;
    for (long long i = 0; i < (n); i++) {
      if (a[i]) {
        o ^= 1;
        f = 1;
      } else {
        if (f) {
          if (o) {
            if (i < n - 1) {
              if (a[i + 1]) {
                ans.emplace_back(i);
                a[i - 1] = 0;
                a[i + 1] = 0;
                long long idx = i - 1;
                while (1) {
                  if (idx < 2) break;
                  if (a[idx - 1] && a[idx - 2]) {
                    ans.emplace_back(idx - 1);
                    a[idx - 2] = 0;
                    a[idx - 1] = 0;
                    idx -= 2;
                  } else
                    break;
                }
                f = 0;
                o = 0;
              } else {
                ans.emplace_back(i);
                a[i] = 1;
                a[i + 1] = 1;
                o = 0;
              }
            }
          } else {
            long long idx = i;
            while (1) {
              if (idx < 2) break;
              if (a[idx - 1] && a[idx - 2]) {
                ans.emplace_back(idx - 1);
                a[idx - 2] = 0;
                a[idx - 1] = 0;
                idx -= 2;
              } else
                break;
            }
            f = 0;
            o = 0;
          }
        }
      }
    }
    if (f) {
      long long idx = n - 1;
      while (idx >= 0) {
        if (a[idx])
          idx--;
        else
          break;
      }
      if (idx >= 0) {
        while (1) {
          if (idx + 2 >= n) break;
          if (a[idx + 1] && a[idx + 2]) {
            ans.emplace_back(idx + 1);
            a[idx + 2] = 0;
            a[idx + 1] = 0;
            idx += 2;
          } else
            break;
        }
      }
    }
    int flag = 1;
    for (long long i = 0; i < (n); i++)
      if (a[i]) flag = 0;
    if (flag) {
      cout << "YES" << endl;
      cout << ans.size() << endl;
      for (long long i = 0; i < (ans.size()); i++)
        cout << ans[i] << (i + 1 == ans.size() ? '\n' : ' ');
    } else
      cout << "NO" << endl;
  }
}

### 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>
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
using namespace std;
template <class T>
using rque = priority_queue<T, vector<T>, greater<T>>;
template <class T>
bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmax(T &a, const T &b) {
  if (b > a) {
    a = b;
    return 1;
  }
  return 0;
}
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  if (b == 0) return a;
  long long cnt = a % b;
  while (cnt != 0) {
    a = b;
    b = cnt;
    cnt = a % b;
  }
  return b;
}
long long extGCD(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
struct UnionFind {
  vector<long long> data;
  int num;
  UnionFind(int sz) {
    data.assign(sz, -1);
    num = sz;
  }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    num--;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  long long size(int k) { return (-data[find(k)]); }
  bool same(int x, int y) { return find(x) == find(y); }
};
template <int mod>
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
long long mpow2(long long x, long long n, long long mod) {
  long long ans = 1;
  while (n != 0) {
    if (n & 1) ans = ans * x % mod;
    x = x * x % mod;
    n = n >> 1;
  }
  return ans;
}
constexpr int mod = 1000000007;
using mint = ModInt<mod>;
mint mpow(mint x, long long n) {
  mint ans = 1;
  while (n != 0) {
    if (n & 1) ans *= x;
    x *= x;
    n = n >> 1;
  }
  return ans;
}
int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  cout << fixed << setprecision(15);
  int T;
  cin >> T;
  while (T--) {
    long long n;
    cin >> n;
    long long a[n];
    for (long long i = 0; i < (n); i++) cin >> a[i];
    vector<long long> ans;
    int f = 0, o = 0;
    for (long long i = 0; i < (n); i++) {
      if (a[i]) {
        o ^= 1;
        f = 1;
      } else {
        if (f) {
          if (o) {
            if (i < n - 1) {
              if (a[i + 1]) {
                ans.emplace_back(i);
                a[i - 1] = 0;
                a[i + 1] = 0;
                long long idx = i - 1;
                while (1) {
                  if (idx < 2) break;
                  if (a[idx - 1] && a[idx - 2]) {
                    ans.emplace_back(idx - 1);
                    a[idx - 2] = 0;
                    a[idx - 1] = 0;
                    idx -= 2;
                  } else
                    break;
                }
                f = 0;
                o = 0;
              } else {
                ans.emplace_back(i);
                a[i] = 1;
                a[i + 1] = 1;
                o = 0;
              }
            }
          } else {
            long long idx = i;
            while (1) {
              if (idx < 2) break;
              if (a[idx - 1] && a[idx - 2]) {
                ans.emplace_back(idx - 1);
                a[idx - 2] = 0;
                a[idx - 1] = 0;
                idx -= 2;
              } else
                break;
            }
            f = 0;
            o = 0;
          }
        }
      }
    }
    if (f) {
      long long idx = n - 1;
      while (idx >= 0) {
        if (a[idx])
          idx--;
        else
          break;
      }
      if (idx >= 0) {
        while (1) {
          if (idx + 2 >= n) break;
          if (a[idx + 1] && a[idx + 2]) {
            ans.emplace_back(idx + 1);
            a[idx + 2] = 0;
            a[idx + 1] = 0;
            idx += 2;
          } else
            break;
        }
      }
    }
    int flag = 1;
    for (long long i = 0; i < (n); i++)
      if (a[i]) flag = 0;
    if (flag) {
      cout << "YES" << endl;
      cout << ans.size() << endl;
      for (long long i = 0; i < (ans.size()); i++)
        cout << ans[i] << (i + 1 == ans.size() ? '\n' : ' ');
    } else
      cout << "NO" << endl;
  }
}

```