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## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Statement

## Goal

You're in the middle of a chase after the famous thief "James".You hear a slamming of a door and realize he has passed through the door to your left.

You run to the door and find a keyboard next to the door that has only two options: true or false.

You notice a bomb on your right and find that you have exactly two minutes to enter the correct answer without exploding, you have only one attempt.

You look for clues and you find a sheet of paper with numbers arranged in the form of a grid and letters arranged in the form of a grid and a sign of plus and a sign of minus next to it.

In that moment you realize what you need to do.

You get 2 grids with the same height and width, one is filled with integers (non-zero) and the other one contains the characters 'X' and '0'. After taking all the integers from the first grid that correspond to an X in the second grid, sequentially row by row and left to right, output

**true**if those integers alternate sign at each step, otherwise output

**false**.

**Example 1:**

`height`= 5,

`width`= 4

12 -1 4 -21

3 8 99 4

96 -92 1 -31

18 -69 -15 26

23 7 -77 -73

X X X X

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

Going row by row and left to right, following the 'X' marks we get this sequence of integers: 12, -1, 4, -21.

We can see that each number has a sign opposite from the previous one :

-1 is

**negative**and the previous one, 12, is

**positive**.

4 is

**positive**and the previous one, -1, is

**negative**.

-21 is

**negative**and the previous one, 4, is

**positive**.

Thus this sequence alternates sign at each step and the output is

**true**.

**Example 2:**

`height`= 3,

`width`= 5

36 324 -140 33 37

115 -289 -225 -372 6

-302 198 -403 -202 48

X X X X X

0 X X X 0

0 0 X 0 0

Going row by row and left to right, following the 'X' marks we get this sequence of integers: 36, 324, -140, 33, 37, -289, -225, -372, -403.

We can see that not each number has a sign opposite from the previous one :

324 is

**positive**and the previous one, 36, is also

**positive**.

Thus this sequence does not alternate sign at each step and the output is

**false**.

**Note:**the examples aligned for ease of understanding.

In real case there is just one space between each integer.

Input

**Line 1**: two space-separated integers : height and width

**Next**: a line of spaced integers (non-zero). (length of line: width)

`height`lines**Next**: a line of spaced characters ('X' or '0'). (length of line: width)

`height`linesOutput

**true**or

**false**.

Constraints

2 ≤

2 ≤

There is no zero in the first grid.

`height`≤ 602 ≤

`width`≤ 90There is no zero in the first grid.

Example

Input

5 4 12 -1 4 -21 3 8 99 4 96 -92 1 -31 18 -69 -15 26 23 7 -77 -73 X X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Output

true

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