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;
const long long int infLL = 9223372036854775806;
const int inf = 2147483646;
const long long int mod = (long long)(998244353);
long long int ceil(long long int a, long long int b) { return (a + b - 1) / b; }
long long int min(long long int a, long long int b) {
  if (a > b)
    return b;
  else
    return a;
}
bool bit_check(long long int a, int i) {
  if ((a & (1LL << i))) return 1;
  return 0;
}
long long int bit_toggle(long long int a, int i) { return (a ^ (1LL << i)); }
long long int bit_sum(long long int a, int i) { return a + (1LL << i); }
long long int bit_sub(long long int a, int i) { return a - (1LL << i); }
long long int mod_power(long long int x, long long int y) {
  long long int p = mod;
  long long int res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long int power_of(long long int a, int b) {
  if (a == 0) return -1;
  return 1 + power_of(a / b, b);
}
long long power(long long int a, long long int b) {
  if (a == 1) return 1;
  long long int res = 1;
  while (b > 0) {
    if (b & 1) res = res * a;
    a = a * a;
    b >>= 1;
  }
  return res;
}
void mycode();
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  mycode();
  return 0;
}
void mycode() {
  int n;
  cin >> n;
  int arr[n + 5];
  long long int x = 0;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    x ^= arr[i];
  }
  if (x != 0 && n % 2 == 0) {
    cout << "NO";
    return;
  }
  cout << "YES\n";
  if (n % 2 == 0) n--;
  cout << n - 2 << '\n';
  cout << 1 << " " << 2 << " " << 3 << '\n';
  for (int i = 2; i + 2 <= n; i += 2) {
    cout << i + 1 << " " << i + 2 << " " << i + 3 << '\n';
    if (i + 3 == n) break;
  }
  for (int i = n - 4; i >= 0; i -= 2)
    cout << i << " " << i + 1 << " " << i + 2 << '\n';
}