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 Sieve(n):

    ret = []
    divlis = [-1] * (n+1)
    
    flag = [True] * (n+1)
    flag[0] = False
    flag[1] = False

    ind = 2
    while ind <= n:

        if flag[ind]:
            ret.append(ind)

            ind2 = ind ** 2

            while ind2 <= n:
                flag[ind2] = False
                divlis[ind2] = ind
                ind2 += ind

        ind += 1

    return ret,divlis


t = int(input())

ret,divs = Sieve(10**6)

for loop in range(t):

    n = int(input())

    ans = []

    now = 1

    flag = False
    
    for i in ret:

        while n % i == 0:
            n //= i
            now *= i

            if now > 1 and now not in ans:
                ans.append(now)
                now = 1

                if len(ans) == 2:
                    if n not in ans and n > 1:
                        ans.append(n)
                        print ("YES")
                        print (" ".join(map(str,ans)))
                        flag = True
                        break
                    else:
                        print ("NO")
                        flag = True
                        break

            if flag:
                break

        if flag:
            break

    if not flag:
        print ("NO")