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 math
def primefactorisation(n):
    p=[]
    while(n%2==0):
        n//=2
        p.append(2)
    i=3
    while(i<=math.sqrt(n)):
        while(n%i==0):
            n//=i
            p.append(i)
        i+=2
    if n>2:
        p.append(n)
    return p

for _ in range(int(input())):
    n=int(input())
    A=primefactorisation(n)
    if len(A)>=3:
        a=A[0]
        b=A[1]
        if b==a:
            b=A[1]*A[2]
        c=n//(a*b)
        if c==a or c==b or c==1:
            print("NO")
        else:
            print("YES")
            print(a," ",b," ",c)
    else:
        print("NO")