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 PYTHON3):

Solution:
import sys
import math
import bisect
from sys import stdin, stdout
from math import gcd, floor, sqrt, log2, ceil
from collections import defaultdict as dd
from bisect import bisect_left as bl, bisect_right as br
from bisect import insort
from collections import Counter
from collections import deque
from heapq import heappush,heappop,heapify
from itertools import permutations,combinations
mod = int(1e9)+7
 
 
ip = lambda : int(stdin.readline())
inp = lambda: map(int,stdin.readline().split())
ips = lambda: stdin.readline().rstrip()
out = lambda x : stdout.write(str(x)+"\n")

t = 1
for _ in range(t):
    n = ip()
    arr = list(inp())
    if n&1 == 1:
        ans = []
        for i in range(0,n-1,2):
            ele = arr[i]^arr[i+1]^arr[i+2]
            arr[i] = ele
            arr[i+1] = ele
            arr[i+2] = ele
            ans.append([i+1,i+2,i+3])
        for i in range(0,n-1,2):
            ans.append([i+1,i+2,n])
            ele = arr[i]^arr[i+1]^arr[n-1]
            arr[i] = ele
            arr[i+1] = ele
            arr[n-1] = ele
        out("YES")
        out(len(ans))
        for i in ans:
            print(*i)
    else:
        xor = 0
        for i in  arr:
            xor ^= i
        if xor == 0:
            ans = []
            for i in range(0,n-2,2):
                ele = arr[i]^arr[i+1]^arr[i+2]
                arr[i] = ele
                arr[i+1] = ele
                arr[i+2] = ele
                ans.append([i+1,i+2,i+3])
            for i in range(0,n-2,2):
                ans.append([i+1,i+2,n-1])
                ele = arr[i]^arr[i+1]^arr[n-2]
                arr[i] = ele
                arr[i+1] = ele
                arr[n-2] = ele
            out("YES")
            out(len(ans))
            for i in ans:
                print(*i)
        else:
            out("NO")