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 ' '*int(input()):
    n = int(input())
    m=n
    p = []
    d = 2
    ln = 0
    x = 0
    while d * d <= n:
        if n % d == 0:
            p.append(d)
            n //= d
            ln += 1
        else:
            d += 1
    if n > 1:
            p.append(n)  
            ln+=1
    #print(p)
    if ln>2:
        a = p[0]
        if p[1]==p[0]:
            b = p[1]*p[2]
            if ln>3 and b!=m//b//a and a!=m//b//a:
                print('YES\n', a,b,m//b//a)
            else:
                print('NO')
        elif p[1]!=m//p[1]//a and a!=m//p[1]//a:
            b = p[1] 
            print('YES\n', a,b,m//b//a)
        else:
            print('NO')
    else:
        print('NO')