human
Monocarp is playing a computer game. Now he wants to complete the first level of this game.

A level is a rectangular grid of 2 rows and n columns. Monocarp controls a character, which starts in cell (1, 1) — at the intersection of the 1-st row and the 1-st column.

Monocarp's character can move from one cell to another in one step if the cells are adjacent by side and/or corner. Formally, it is possible to move from cell (x_1, y_1) to cell (x_2, y_2) in one step if |x_1 - x_2| ≤ 1 and |y_1 - y_2| ≤ 1. Obviously, it is prohibited to go outside the grid.

There are traps in some cells. If Monocarp's character finds himself in such a cell, he dies, and the game ends.

To complete a level, Monocarp's character should reach cell (2, n) — at the intersection of row 2 and column n.

Help Monocarp determine if it is possible to complete the level.

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Then the test cases follow. Each test case consists of three lines.

The first line contains a single integer n (3 ≤ n ≤ 100) — the number of columns.

The next two lines describe the level. The i-th of these lines describes the i-th line of the level — the line consists of the characters '0' and '1'. The character '0' corresponds to a safe cell, the character '1' corresponds to a trap cell.

Additional constraint on the input: cells (1, 1) and (2, n) are safe.

Output

For each test case, output YES if it is possible to complete the level, and NO otherwise.

Example

Input

4
3
000
000
4
0011
1100
4
0111
1110
6
010101
101010

Output

YES
YES
NO
YES

Note

Consider the example from the statement.

In the first test case, one of the possible paths is (1, 1) → (2, 2) → (2, 3).

In the second test case, one of the possible paths is (1, 1) → (1, 2) → (2, 3) → (2, 4).

In the fourth test case, one of the possible paths is (1, 1) → (2, 2) → (1, 3) → (2, 4) → (1, 5) → (2, 6).
Solve the task in PYTHON3.

Can you provide a Python program to determine if it is possible to complete the level?
assistant
#Here is Python program to determine if it is possible to complete the level.

t = int(input())
from collections import deque
 
for caseNr in range(1, t + 1):
    n = int(input())
    #n, H = list(map(int, input().split()))
    #row1 = list(map(int, input().split()))
    #row2 = list(map(int, input().split()))
    #arr = list(input())
    #print(arr)
    #c = Counter(arr)
    row1 = input()
    row2 = input()
    
    matrix = [[] for _ in range(2)]
    matrix[0] = [int(row1[i]) for i in range(len(row1))]
    matrix[1] = [int(row2[i]) for i in range(len(row2))]
    
    
    queue = deque([(0,0)])
    visited = set()
    dirs = [[1,0],[-1,0],[0,1],[0,-1],[1,1],[-1,1],[1,-1],[-1,-1]]
    def find_neighbours(cur):
        res = []
        for dir1 in dirs:
            if 0 <= cur[0] + dir1[0] <= 1 and  0 <= cur[1] + dir1[1] <= len(matrix[0])-1 and matrix[cur[0] + dir1[0]][cur[1] + dir1[1]] != 1:
                res.append([cur[0]+dir1[0],cur[1]+dir1[1]])    
        return res
    
    ans = "NO"
    while queue:
        cur = queue.popleft()
        #print(cur)
        #type(cur)
        if cur[0] == 1 and cur[1] == len(matrix[1])-1:
            ans = "YES"
            break
        
        for neighbour in find_neighbours(cur):
            if tuple(neighbour) not in visited:
                visited.add(tuple(neighbour))
                queue.append(tuple(neighbour))
    
    print(ans)