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 collections import defaultdict as dd
def facts(x):
    f=set()
    for i in range(2,int(x**0.5)+1):
        if x%i==0:
            f.add(i)
            f.add(x//i)
    return list(f)

for _ in range(int(input())):
    n=int(input())
    fac=facts(n)
    if len(fac)<3:
        print('NO')
    else:
        have=dd(lambda:False)
        
        root=n**0.5
        for x in fac:
            have[x]=True
        done=False
        for i in range(len(fac)):
            for j in range(i+1,len(fac)):
                x,y=fac[i],fac[j]
                z=n//(x*y)
                if z==x or z==y:
                    continue
                if have[z]==True and x*y*z==n:
                    done=True
                    print('YES')
                    print(x,y,z)
                    break
            if done:
                break
                
        if not done:
            print('NO')