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 functools import reduce

def fac(n):
    return sorted(set(reduce(list.__add__,
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))

t=int(input())
for i in range(t):
    n=int(input())
    x=fac(n)

    x=x[1:-1]

    flag=1
    if len(x)<3:
        flag=0
    else:
        a,b=x[0],0
        for j in range(1,len(x)):
            if n%(a*x[j])==0:
                b=x[j]
                break
        if b:
            te=a*b
            if n%te==0:
                c=n//te
                if a!=b and a!=c and b!=c and a>=2 and b>=2 and c>=2:
                    pass
                else:
                    flag=0
            else:
                flag=0
        else:
            flag=0

    if flag:
        pass
        print("YES")
        print(a,b,c)
    else:
        print("NO")