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:
number_test = int(input())

lista = []

for test in range(number_test):

    numbers = input()
    numbers_list = [int(number) for number in numbers.split()]
    nmax = numbers_list.count(max(numbers_list))
    numbers_list.sort(reverse=True)
    list_answer = []

    if nmax < 2:
        list_answer.append("NO")
        lista.append(list_answer)
    else:
        list_answer.append("YES")
        a = max(numbers_list)
        b = numbers_list[2]
        list_answer.append(str(a))
        list_answer.append(str(b))

        if (numbers_list[0] == numbers_list[2]):
            list_answer.append(str(b))
        else:
            for c in range(b + 1):
                if (c != 0) and (c <= b):
                    list_answer.append(str(c))
                    break
        lista.append(list_answer)

for nums in lista:
    if len(nums) != 1:
        print(nums[0])
        print(' '.join(nums[1:]))
    else:
        print(nums[0])