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 q in range(t):
    n=int(input())
    i1=1
    j1=1
    k1=1
    q=int(n**0.5)
    for i in range(2,q):
        if n%i==0:
            i1=i
            break
    if i1!=1:
        n=n//i1
        for j in range(i1+1,q):
            if n%j==0:
                j1=j
                break
        if j1!=1:
            n=n//j1
            if n>j1 and n>i1 :
                print("YES")
                print(i1,j1,n)
            else:
                print("NO")
        else:
            print("NO")
    else:
        print("NO")