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:
t=int(input())
for i in range(t):
    n=int(input())
    k1=int(pow(n,0.333))
    k2=k1**2
    a=0
    b=0
    s=n
    for j in range(2,k1+1):
        if(n%j==0):
            a=j
            n=n//j
            break
    if(a==0):
        print ('NO')
        continue
    else:
        k=int(pow(n,0.5))
        for j in range(a+1,k+1):
            if(n%j==0):
                b=j
                n=n//j
                break
    if(b==0):
        print ('NO')
        continue
    else:
        c=s//(a*b)
        if(c==1 or c==a or c==b):
            print ('NO')
        else:
            print ('YES')
            print (a,end=" ")
            print (b,end=" ")
            print (c)