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:
q = int(input())

def div_by_primes(n):
    p = []
    s = []
    for d in range(2, int(n**(1/2))+1):
        if n%d == 0:
            p.append(d)
            s.append(0)
            while n%d == 0:
                s[-1] += 1
                n //= d
    if n > 1:
        p.append(n)
        s.append(1)
    return p, s

def s_mult(s, p):
    ans = 1
    for i in range(len(s)):
        ans *= p[i]**s[i]
    return ans

for _ in range(q):
    n = int(input())
    p, s = div_by_primes(n)
    if len(p) == 1:
        if s[0] < 6:
            print("NO")
        else:
            print("YES\n", p[0], p[0]**2, p[0]**(s[0]-3))
    elif len(p) == 2:
        if s[0]+s[1] < 4:
            print("NO")
        elif s[0] == 1:
            print("YES\n", p[0], p[1], p[1]**(s[1]-1))
        elif s[1] == 1:
            print("YES\n", p[0], p[1], p[0]**(s[0]-1))
        else:
            print("YES\n", p[0], p[1], p[0]**(s[0]-1)*p[1]**(s[1]-1))
    else:
        print("YES\n", p[0]**s[0], p[1]**s[1], s_mult(s[2:], p[2:]))