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:
def getFacts(n):
    facts = []
    for i in range(2,int(n**0.5)+1):
        if n%i == 0:
            facts.append(i)
            if i != n//i:
                facts.append(n//i)

    return facts

def solve(n):
    facts = getFacts(n)
    for i in range(len(facts)):
        a = facts[i]
        bc = n//a
        f = getFacts(bc)
        for k in f:
            b = k
            c = bc//k
            if a != b and b != c and a != c:
                print('YES')
                print(a,b,c)
                return

    print('NO')

def main():
    t = int(input())
    for i in range(t):
        n = int(input())
        solve(n)

        
main()