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 getSmallestFactor(n,d):

    for i in range(2,int(n**0.5)+1):

        if i not in d and n%i==0:
            return i

    return -1

t = int(input())

for _ in range(t):

    n = int(input())

    sm1 = getSmallestFactor(n,{})
    if sm1!=-1:
        sm2 = getSmallestFactor(n//sm1,{sm1})
        sm3 = n//(sm1*sm2)
        if sm2!=-1 and sm3 not in [sm1,sm2,1]:
            print('YES')
            print(sm1,sm2,sm3)
        else:
            print('NO')
    else:
        print('NO')