Problem: You are given three positive (i.e. strictly greater than zero) integers x, y and z.

Your task is to find positive integers a, b and c such that x = max(a, b), y = max(a, c) and z = max(b, c), or determine that it is impossible to find such a, b and c.

You have to answer t independent test cases. Print required a, b and c in any (arbitrary) order.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains three integers x, y, and z (1 ≤ x, y, z ≤ 10^9).

Output

For each test case, print the answer:

  * "NO" in the only line of the output if a solution doesn't exist; 
  * or "YES" in the first line and any valid triple of positive integers a, b and c (1 ≤ a, b, c ≤ 10^9) in the second line. You can print a, b and c in any order. 

Example

Input


5
3 2 3
100 100 100
50 49 49
10 30 20
1 1000000000 1000000000


Output


YES
3 2 1
YES
100 100 100
NO
NO
YES
1 1 1000000000

Solution (in PYTHON3):

Solution:
import heapq as hp
import collections
import bisect


def unpack(func=int):
    return map(func, input().split())


def l_unpack(func=int):
    """list unpack"""
    return list(map(func, input().split()))


def s_unpack(func=int):
    """sorted list unpack"""
    return sorted(map(func, input().split()))


def range_n():
    return range(int(input()))


def getint():
    return int(input())


def foo(s, l, r, c, memo):
    t = l, r, c
    if t in memo:
        return memo[t]
    ans = 0
    if l == r:
        return 1 if s[l] != c else 0
    half = (r - l + 1) // 2
    a = abs(s[l:l + half].count(c) - half)
    b = abs(s[r - half + 1:r + 1].count(c) - half)
    ans += min(a + foo(s, l + half, r, chr(ord(c) + 1), memo),
               b + foo(s, l, l + half - 1, chr(ord(c) + 1), memo)
               )
    memo[t] = ans
    return ans


def main():
    for _ in range_n():
        x, y, z = unpack()
        if x != y and y != z and x != z:
            print('NO')
        else:
            if x == z and x >= y:
                print('YES')
                print(y, y, x)
            elif x == y and x >= z:
                print('YES')
                print(z, z, x)
            elif y == z and y >= x:
                print('YES')
                print(x, x, z)
            else:
                print('NO')


main()