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brute force

dfs and similar

dp

implementation

*800

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A. Computer Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMonocarp 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 $$$|x_1 - x_2| \le 1$$$ and $$$|y_1 - y_2| \le 1$$$. 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 $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. Then the test cases follow. Each test case consists of three lines.

The first line contains a single integer $$$n$$$ ($$$3 \le n \le 100$$$) — 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 $$$(1, 1) \rightarrow (2, 2) \rightarrow (2, 3)$$$.

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

In the fourth test case, one of the possible paths is $$$(1, 1) \rightarrow (2, 2) \rightarrow (1, 3) \rightarrow (2, 4) \rightarrow (1, 5) \rightarrow (2, 6)$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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