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:
from sys import stdin
input=stdin.readline
#a=[]
import math
def com(p,q,r):
    if p==q or q==r or p==r:
        return -1
    else:
        return 1
def pd(n) : 
    t=[]
    i = 1
    while i <= math.sqrt(n): 
          
        if (n % i == 0 and i!=1) :
            if (n // i == i) : 
                t.append([i,i])
            else : 
                t.append([i,n//i]) 
        i+=1
    return t    
for _ in range (int(input())):
    n=int(input()) 
    a=pd(n)
    ans=-1
    for i in range(len(a)):
        if ans==1:
            break
        x=a[i][0]
        y=a[i][1]
        b=pd(x)
        c=pd(y)
        for i in range(len(b)):
            ans = com(b[i][0],b[i][1],y)
            if ans==1:
                ans1=[b[i][0],b[i][1],y]
                break
        if ans==1:
            break
        for i in range(len(c)):
            ans = com(c[i][0],c[i][1],x)
            if ans==1:
                ans1=[c[i][0],c[i][1],x]
                break
    if ans==1:
        print('YES')
        print(*ans1)
    else:
        print('NO')