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 factors(n):
    factor = []
    for i in range(2, int(n**0.5)+1):
        if n % i == 0:
            factor.append(i)
    return factor


t = int(input())
for l in range(t):
    n = int(input())
    x = 0
    factor = factors(n)
    lenfactor = len(factor)
    for i in range(lenfactor):
        for j in range(i+1, lenfactor):
            k = n/(factor[i]*factor[j])
            if k%1 == 0 and k != factor[i] and k != factor[j]:
                print('YES')
                print(str(factor[i]) + ' ' + str(factor[j]) + ' ' + str(int(k))  )
                x = 1 
                break
        if x == 1:
            break
    if x == 0:
        print('NO')