Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in PYTHON3):

Solution:
import sys
sys.setrecursionlimit(10**9)
IA =lambda: map(int,input().split())
ans=[0,0,0,0]
def solve(n):
    num=int(0)
    i=int(2)
    tmp=1
    m=n
    while i*i<=m:
        if n%i==0:
            n=n//i
            tmp*=i
            if tmp not in ans:
                num+=1
                ans[num]=tmp
                tmp=1
                if num>=3:
                    ans[num]*=n
                    return 1
            
        i+=1
    if n>1:
        if tmp*n not in ans:
            num+=1
            ans[num]=n*tmp
    if num>=3: return 1
    else:return -1
        
    

T=int(input())
for t in range(0,T):
    ans=[0,0,0,0]
    n=int(input())
    if solve(n)==1:
        print("YES")
        for i in range(1,4):
            print(ans[i],end=" ")
        print()
    else:print("NO")