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:
"""
    Template written to be used by Python Programmers.
    Use at your own risk!!!!
    Owned by adi0311(rating - 1989 at CodeChef and 1405 at CodeForces).
"""

import sys
from bisect import bisect_left as bl, bisect_right as br, bisect  # Binary Search alternative
import math
from timeit import default_timer as dt  # To get the running time of a program
from itertools import zip_longest as zl  # zl(x, y) return [(x[0], y[0]), ...]
from itertools import groupby as gb  # gb(x, y)
from itertools import combinations as comb  # comb(x, y) return [all subsets of x with len == y]
from itertools import combinations_with_replacement as cwr
from collections import defaultdict as dd  # defaultdict(<datatype>) Free of KeyError.
from collections import deque as dq  # deque(list) append(), appendleft(), pop(), popleft() - O(1)
from collections import Counter as c  # Counter(list)  return a dict with {key: count}
# sys.setrecursionlimit(2*pow(10, 6))
# sys.stdin = open("input.txt", "r")
# sys.stdout = open("output.txt", "w")
mod = pow(10, 9) + 7
mod2 = 998244353
# def data(): return sys.stdin.readline().strip()
# def out(var): sys.stdout.write(var)
def data(): return input()
def l(): return list(sp())
def sl(): return list(ssp())
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [[val for i in range(n)] for j in range(m)]


def factors(n):
    s = set()
    i = 2
    while i <= math.sqrt(n):
        if n % i == 0:
            s.add(n//i)
            s.add(i)
        i += 1
    return s

for _ in range(int(data())):
    n = int(data())
    ans = factors(n)
    if len(ans) < 3:
        print("NO")
    else:
        r = False
        for i in ans:
            for j in ans:
                if i != j:
                    if n//(i*j) == n/(i*j) and n//(i*j) != 1 and n//(i*j) != i and n//(i*j) != j:
                        print("YES")
                        print(i, j, n//(i*j))
                        r = True
                        break
            if r:
                break
        if not r:
            print("NO")