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(0,int(input())):
    n=int(input())
    f1=0
    f2=0
    root=int(n**0.5)
    for i in range(2,root+1):
        if n%i==0:
            k=i
            f1=1
            break
    if f1==1:
        n=int(n/k)
        root=int(n**0.5)
        k1=k
        for i in range(2,root+1):
            if n%i==0 and i*i!=n and i!=k1:
                k=i
                f2=1
                break
        if f2==1:
            print("YES")
            print(k1,k,int(n/k))
        else:
            print("NO")
    else:
        print("NO")