DMOPC '19 Contest 2 P2 - Squares

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Points: 7
Time limit: 3.0s
Memory limit: 64M

Problem type

You are given an N \times M grid of squares. Each square contains a number a_i, 1 \le i \le N \times M, the cost to travel through that square. You are starting at the most top-left square. At each turn you may choose to move down or right but not both. Find the minimum cost it would take you to travel to the most bottom-right square.


In all tests,
2 \le N, M \le 500
1 \le a_i \le 10^6

Input Specification

The first line contains two integers, N and M, the dimensions of the grid of squares (N rows and M columns).
The next N lines each contains M integers, a_i, the cost to travel through that square in the grid.

Output Specification

Output on a single line, the minimum sum of costs to travel from the most top-left square to the most bottom-right square.

Sample Input

3 4
3 1 2 4
9 8 7 6
2 8 9 2

Sample Output


Explanation for Sample Output

We can take the path 3 \to 1 \to 2 \to 4\to 6 \to 2, which gives us the sum of 18. There are no paths that yield a smaller sum.


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