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())
    a=0
    b=0
    c=0
    for i in range(2,int(n**0.5)+2):
        if n%i==0:
            n//=i
            a=i
            break
    if a==0:
        print("NO")
        continue
    else:
        for j in range(a+1,int(n**0.5)+2):
            if n%j==0 and n//j!=j and n//j!=a:
                b=j
                c=n//j
                break
        if b==0:
            print("NO")
            continue
        else :
            print("YES")
            print(a,b,c)