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 primeFactors(n):
    a = []
    while n % 2 == 0: 
        a.append(2) 
        n = n // 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            a.append(i)
            n = n//i 
    if n > 2: 
        a.append(n)
    return a

t = int(input())
for _ in range(t):
    n = int(input())
    k = primeFactors(n)
    l = len(k)
    w = len(set(k))
    if l>=6:
        p=1
        print("YES")
        for i in range(3,l):
            p*=k[i]
        print(k[0],k[1]*k[2],p)
    elif l<=2:
        print("NO")
    elif l==3:
        if w==3:
            print("YES")
            print(k[0],k[1],k[2])
        else:
            print("NO")
    else:
        if w==1:
            print("NO")
        else:
            print("YES")
            k.sort()
            if l==4:
                print(k[0],k[1]*k[2],k[3])
            else:
                print(k[0],k[1]*k[2]*k[3],k[4])