Minimum path sum

Given a grid of height h and width w filled with integers, you are asked to find a path from the top-left to the bottom-right corner that minimizes the sum of numbers along the path. You are only allowed to move right or down.
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 3 2 1 3 1 9 2 3 9 1 5 4

Input

The first line of the input contains two integers h and w (1 β€ h, w β€ 1000).
The next h lines contain w space-separated integers representing the values in the grid .

Output

The program should print the minimum possible sum to get from the top-left corner to the bottom-right corner.

Examples

 Input Output 3 4 3 2 1 3 1 9 2 3 9 1 5 4 15

Explanation

We can move: 3 β 2 β 1 β 2 β 3 β 4
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Hint 1
The state in a dynamic programming problem can be a 2-dimensional array.
Hint 2
It can represent the best possible solution up to that coordinate (d[r][c] represents the best path to reach the row r and the column c).
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Why doesnβt the greedy approach work here? Imagine if you always moved in the direction of the smallest possible value. What would be the issue there?
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Constraints

Time limit: 3 seconds

Memory limit: 512 MB

Output limit: 1 MB