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 p3n(cur):
    j = 2
    while j * j <= cur:
        if cur % j == 0:
            # print(cur, j)
            oth = cur // j
            k = 2
            while k * k <= oth:
                if oth % k == 0 and j != k != oth // k != j:
                    print('YES')
                    print(j, k, oth // k)
                    return
                k += 1
        j += 1
    print('NO')


t = int(input())
tc = []
for i in range(t):
    tc.append(int(input()))
for i in range(t):
    p3n(tc[i])