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 
import math
for i in range(int(input())):
    q=int(input())
    k=[]
    t=0
    for i in range(2,int(math.sqrt(q))+1):
        if q%i==0:
            q=q//i
            t=1
            k.append(str(i))
            break
    if t==1:
        for i in range(2,int(math.sqrt(q))+1):
            if q%i==0 and (str(i) not in k):
                q=q//i
                t=2
                k.append(str(i))
                break
    else:
        print('NO')
    if t==2 and str(q) not in k:
        k.append(str(q))
        print('YES')
        print(' '.join(k))
    elif t!=0:
        print('NO')