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:
pr = [1]*40000
primes = []
for i in range(2, 40000):
    if pr[i]:
        primes.append(i)
        for j in range(i*i, 40000, i):
            pr[j] = 0



def sl(a,b,kkk):
    print("YES")
    print(a,b,kkk//(a*b))



n = int(input())
for i in range(n):
    k = int(input())
    kk = k
    f = []
    for p in primes:
        if k % p == 0:
            f.append([p,1])
            k //= p
            while k % p == 0:
                f[-1][1] += 1
                k //= p
            if len(f) > 2:
                break
        if p*p >= kk:
            break

    if k != 1:
        f.append([k,1])
    # print(f)
    if len(f) >= 3:
        # print("YES")
        sl(f[0][0], f[1][0], kk)
    elif len(f) == 2:
        if f[0][1] >= 2 and f[1][1] >= 2:
            sl(f[0][0], f[1][0], kk)
        elif f[0][1] >= 3:
            sl(f[0][0], f[0][0] * f[0][0], kk)
        elif f[1][1] >= 3:
            sl(f[1][0], f[1][0] * f[1][0], kk)
        else:
            print("NO")
    else:
        if f[0][1] >= 6:
            sl(f[0][0], f[0][0] * f[0][0], kk)
        else:

            print("NO")