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:
for i in range(int(input())):
    a=int(input())
    r=0
    b=1
    while(1):
        p=0
        for j in range(b+1,a+1):
            if a//j<=j:
            	p=1
            	break
            else:
                if a%j==0:
                    if r==1:
                        c=j
                        d=a//j
                        p=1
                        r+=2
                        break
                    else:
                        b=j
                        a=a//b
                        r+=1
        if p==1:
            break
    if r==3:
        print('yes'.upper())
        print(b,c,d)
    else:
        print('no'.upper())