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:
t = int(input())
for i in range(t):
    n = int(input())
    m = [0, 0, 0]
    k = 0
    for j in range(2, int(n ** 0.5) + 1):
        if n % j == 0 and j not in m:
            m[k] = j
            k += 1
            n //= j
        if k == 2 or j > n:
            break
    if k == 2 and n not in m:
        m[2] = n
    if m[0] and m[1] and m[2]:
        print("YES")
        print(m[0], m[1], m[2])
    else:
        print("NO")