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 factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n ** 0.5 // 1)) + 1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            for j in range(cnt):
                arr.append(i)

    if temp != 1:
        arr.append(temp)

    if arr == []:
        arr.append(n)

    return arr
n = int(input())
for _ in range(n):
    x = int(input())
    dat = factorization(x)
    datlen = len(dat)
    #print("--")
    #print(x)
    #print(l)
    if len(dat) <= 2:
        print("NO")
    else:
        f = False
        a = 1
        for i in range(datlen):
            a *= dat[i]
            b = 1
            for j in range(i+1, datlen):
                b *= dat[j]
                c = 1
                for k in range(j+1, datlen):
                    c *= dat[k]
                if a != b and b != c and a != c and a != 1 and b != 1 and c != 1:
                    f = True
                    break
            if f:
                break
        if f:
            print("YES")
            print("{0} {1} {2}".format(a, b, c))
        else:
            print("NO")