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 factor(x):
    p = []
    d = 2
    while d * d <= x:
        if x % d == 0:
            p.append(d)
            x //= d
        else:
            d += 1
    if x > 1:
        p.append(x)
    return p


t = int(input())
for i in range(t):
    n = int(input())
    p = factor(n)
    a, b, c = 1, 1, 1
    ans = 'NO'
    if len(p) > 2:
        a = p[0]
        if p[1] != p[0]:
            b = p[1]
            c = 1
            for k in p[2:]:
                c *= k
            if c != 1 and c != b and c != a:
                ans = 'YES'
        else:
            b = p[1] * p[2]
            c = 1
            for k in p[3:]:
                c *= k
            if c != 1 and c != b and c != a:
                ans = 'YES'

    if ans == 'YES':
        print('YES')
        print(a, b, c)
    else:
        print('NO')