human
PYTHON3 solution for "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).":


 Can you provide a Python code to determine if it is possible to complete the level?
assistant
#Here is Python code to determine if it is possible to complete the level.
 def game(n):
    n=n-1;
    mtx = []
    a = str(input())
    mtx.append(a);
    b=str(input())
    mtx.append(b);

    stk = []
    stk.append([0, 0]);

    visit = [[], []]
    for i in range(2):
        for j in range(n+1):
            visit[i].append(False)

    visit[0][0]==True

    while (len(stk)!=0):
        x = stk.pop()
        
        if (x[0]>1 or x[0]<0 or x[1]>n or x[1]<0):
            continue;

        if (x[0]==0):
            if (mtx[0][x[1]]=="0"):
                if (visit[1][x[1]]==False):
                    stk.append([1, x[1]])
                    visit[1][x[1]] = True;
        if (x[0]==1):
            if (mtx[1][x[1]]=="0"):
                if (visit[0][x[1]]==False):
                    stk.append([0, x[1]])
                    visit[0][x[1]] = True;
        
        if (x[1]<n):
            if (mtx[x[0]][x[1]+1]=="0"):
                if (visit[x[0]][x[1]+1]==False):
                    stk.append([x[0], x[1]+1])
                    visit[x[0]][x[1]+1] = True;
        
        if (x[1]>0):
            if (mtx[x[0]][x[1]-1]=="0"):
                if (visit[x[0]][x[1]-1]==False):
                    stk.append([x[0], x[1]-1])
                    visit[x[0]][x[1]-1] = True;

    return visit[1][n];

for _ in range(int(input())):
    flg = game(int(input()))

    if flg:
        print("YES")
    else:
        print("NO")