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 _ in range(int(input())):
    n=int(input())
    l=[]
    a=2
    m=n
    while a*a<=n:
        if(n%a==0):
            l.append(a)
            n=n//a
            break
        a+=1
    b=2
    while b*b<=n:
        if(n%b==0):
            if b not in l:
                l.append(b)
                n=n//b
                break
        b+=1
    if(len(l)==2):
        c=m//(l[0]*l[1])
        if c not in l:
            print("YES")
            print(l[0],l[1],c)
        else:
            print("NO")
    else:
        print("NO")