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 
# Problem C
T = int(input())
for _ in range(T):
    n = int(input())
    a = 0
    b = 0
    c = 0
    for i in range(2, int(n**0.5)):
        if n % i == 0:
            a = i
            break
        else:
            continue
    if a != 0:
        for i in range(a+1, int(n**0.5)):
            if n/a % i == 0:
                b = i
                c = int(n/(a*b))
                break
            else:
                continue
    if c > 1 and b != c and a!= c:
        print("YES")
        print(a,b,c)
    else:
        print("NO")