# Maximum falling path sum

Given a grid of height `h` and width `w`, you are asked to calculate the maximum sum one might obtain by moving from top to bottom, where on each step itβs only allowed to move to the below adjacent 3 cells. In other words, being at position `(r, c)`, you can move to positions: `(r + 1, c - 1)`, `(r + 1, c)`, and `(r + 1, c + 1)`. Thatβs why we call it a falling sum - as we fall from the top to the very bottom of the grid. Find the maximum sum of the path.
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#### Input

The first line of the input contains two integers `h` and `w` (1 β€ h, w β€ 100).
The next `h` lines contain `w` numbers (-100 β€ β€ 100) representing the values of the grid at row `r` and column `c`.

#### Output

The program should print the maximum possible sum obtained among all the possible falling paths.

#### Examples

 Input Output 3 3 2 1 3 6 5 4 7 8 9 17
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#### Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB