A tax collector must travel through an N × M dungeon to collect revenue records.

Each cell in the dungeon affects the collector's Health Points (HP):

• A positive value increases HP.
• A negative value decreases HP.
• 0 has no effect.

The collector starts at the top-left cell (0,0) and must reach the bottom-right cell (N-1, M-1).

At every step, the collector may move only:

• Right
• Down

The collector's HP must never drop to 0 or below at any point during the journey.

Determine the minimum initial HP required to guarantee survival until reaching the destination.

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Input Format

• The first line contains an integer N, representing the number of rows.
• The second line contains an integer M, representing the number of columns.
• The next N lines each contain M space-separated integers representing the dungeon grid.

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Output Format

Print a single integer representing the minimum initial HP required.

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Constraints

• 1 ≤ N, M ≤ 200
• -1000 ≤ dungeon[i][j] ≤ 1000

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Sample Input

3
3
-2 -3 3
-5 -10 1
10 30 -5

Sample Output

7

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Explanation

Starting with 7 HP, one optimal path is:

(0,0) → (0,1) → (0,2) → (1,2) → (2,2)

HP during the journey:

7 → 5 → 2 → 5 → 6 → 1

The HP never becomes 0 or negative, so the minimum required initial HP is 7.