Problem: Ksenia has an array a consisting of n positive integers a_1, a_2, …, a_n. 

In one operation she can do the following: 

  * choose three distinct indices i, j, k, and then 
  * change all of a_i, a_j, a_k to a_i ⊕ a_j ⊕ a_k simultaneously, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). 



She wants to make all a_i equal in at most n operations, or to determine that it is impossible to do so. She wouldn't ask for your help, but please, help her!

Input

The first line contains one integer n (3 ≤ n ≤ 10^5) — the length of a.

The second line contains n integers, a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — elements of a.

Output

Print YES or NO in the first line depending on whether it is possible to make all elements equal in at most n operations.

If it is possible, print an integer m (0 ≤ m ≤ n), which denotes the number of operations you do.

In each of the next m lines, print three distinct integers i, j, k, representing one operation. 

If there are many such operation sequences possible, print any. Note that you do not have to minimize the number of operations.

Examples

Input


5
4 2 1 7 2


Output


YES
1
1 3 4

Input


4
10 4 49 22


Output


NO

Note

In the first example, the array becomes [4 ⊕ 1 ⊕ 7, 2, 4 ⊕ 1 ⊕ 7, 4 ⊕ 1 ⊕ 7, 2] = [2, 2, 2, 2, 2].

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long powmod(long long a, long long b, long long MOD) {
  if (a == 0ll) {
    return 0ll;
  }
  a %= MOD;
  long long ans = 1;
  while (b) {
    if (b & 1) {
      ans = ans * a % MOD;
    }
    a = a * a % MOD;
    b >>= 1;
  }
  return ans;
}
long long poww(long long a, long long b) {
  if (a == 0ll) {
    return 0ll;
  }
  long long ans = 1;
  while (b) {
    if (b & 1) {
      ans = ans * a;
    }
    a = a * a;
    b >>= 1;
  }
  return ans;
}
void Pv(const vector<int> &V) {
  int Len = int(V.size());
  for (int i = 0; i < Len; ++i) {
    printf("%d", V[i]);
    if (i != Len - 1) {
      printf(" ");
    } else {
      printf("\n");
    }
  }
}
void Pvl(const vector<long long> &V) {
  int Len = int(V.size());
  for (int i = 0; i < Len; ++i) {
    printf("%lld", V[i]);
    if (i != Len - 1) {
      printf(" ");
    } else {
      printf("\n");
    }
  }
}
inline long long readll() {
  long long tmp = 0, fh = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') fh = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') tmp = tmp * 10 + c - 48, c = getchar();
  return tmp * fh;
}
inline int readint() {
  int tmp = 0, fh = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') fh = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') tmp = tmp * 10 + c - 48, c = getchar();
  return tmp * fh;
}
void pvarr_int(int *arr, int n, int strat = 1) {
  if (strat == 0) {
    n--;
  }
  for (int i = strat; i <= n; i++) {
    printf("%d%c", arr[i], i == n ? '\n' : ' ');
  }
}
void pvarr_LL(long long *arr, int n, int strat = 1) {
  if (strat == 0) {
    n--;
  }
  for (int i = strat; i <= n; i++) {
    printf("%lld%c", arr[i], i == n ? '\n' : ' ');
  }
}
const int maxn = 1000010;
const int inf = 0x3f3f3f3f;
int a[maxn];
int n;
std::vector<int> v[maxn];
map<int, int> vis;
set<int> st[maxn];
int main() {
  n = readint();
  int id = 0;
  for (int i = 1; i <= n; i++) {
    a[i] = readint();
  }
  int xorsum = 0;
  for (int i = 1; i <= n; i++) {
    xorsum ^= a[i];
  }
  if (xorsum != 0 && (n % 2) == 0) {
    printf("NO\n");
  } else {
    std::vector<pair<pair<int, int>, int>> v;
    if (n & 1) {
      for (int i = 1; i + 2 <= n; i += 2) {
        v.push_back(make_pair(make_pair(i, i + 1), i + 2));
      }
      for (int i = 1; i + 2 <= n - 1; i += 2) {
        v.push_back(make_pair(make_pair(i, i + 1), n));
      }
    } else {
      for (int i = 1; i + 2 <= n - 1; i += 2) {
        v.push_back(make_pair(make_pair(i, i + 1), i + 2));
      }
      for (int i = 1; i + 2 <= n - 2; i += 2) {
        v.push_back(make_pair(make_pair(i, i + 1), n));
      }
    }
    printf("YES\n");
    printf("%d\n", int(v.size()));
    for (auto x : v) {
      printf("%d %d %d\n", x.first.first, x.first.second, x.second);
    }
  }
  return 0;
}