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:
######################################################
############Created by Devesh Kumar###################
#############devesh1102@gmail.com####################
##########For CodeForces(Devesh1102)#################
#####################2020#############################
######################################################
 
 
 
import sys 
import heapq 
import copy
import math
import decimal
input = sys.stdin.readline
# import sys.stdout.flush as flush
# from decimal import *
#heapq.heapify(li) 
#
#heapq.heappush(li,4) 
#
#heapq.heappop(li)
#
# &    Bitwise AND Operator    10 & 7 = 2
# |    Bitwise OR Operator    10 | 7 = 15
# ^    Bitwise XOR Operator    10 ^ 7 = 13
 
# <<    Bitwise Left Shift operator    10<<2 = 40
# >>    Bitwise Right Shift Operator
# '''############ ---- Input Functions ---- #######Start#####'''
# n = 100
# parent = [-1 for i in range(n)]
# def find(a):
#     if parent[a] == a:
#         return a
#     else:
#         parent[a] = find(parent[a])
    
# def union(a,b):
 
 
 
 
    # print(lsp )
def inp():
    return(int(input()))
def inlt(): 
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def insr2():
    s = input()
    s = list(s[:len(s) - 1])
    s = [ord(s[i]) - ord("a") for i in range(len(s))]
    return s
def invr():
    return(map(int,input().split()))
############ ---- Input Functions ---- #######End
# #####   
 
 
ans = 0
def pr_list(a):
    print( *a , sep=" ")
 
def swap(a,b):
    temp = a
    a = b
    b = temp
    return [ a,b]
    # return [b,a]
mod = 1000000007
def pri(a,b):
    s = "? " + str(a) + " " + str(b)
    print(s)
    sys.stdout.flush()
def solve():
    n = inp()
    a = inlt()
    ans = []
    for i in range( 2,n,2):
        dum = a[i-2]^a[i-1]^a[i]
        a[i-2] = dum
        a[i-1] = dum
        a[i] = dum
        ans.append([i-1,i,i+1])
    if n%2 == 0:
        if a[n-1] != a[n-2]:
            print("NO")
            return
        n = n -1
    for i in range(n-3,1,-2):
        dum = a[i-2]^a[i-1]^a[i]
        a[i-2] = dum
        a[i-1] = dum
        a[i] = dum
        ans.append([i-1,i,i+1])

    print("YES")
    # print(a) /
    print(len(ans))
    for i in ans:
        pr_list(i)
    # pr_list(a)
    return
def main():
    tests = 1
    # tests =  inp()

    
    limit = 10**18
    ans = 0
    stack = []
    hashm = {}
    arr = []
    heapq.heapify(arr) 
 
    for test in range(tests):
        solve()
 
        
 
 
if __name__== "__main__":
    main()