Most Stones Removed

Stones are placed on the integer grid, stones[i] = [x, y], at most one per cell. You may remove a stone if there is another stone in the same row or the same column that has not been removed. Return the largest number of stones you can remove.

For [[0, 0], [0, 1], [1, 0], [1, 2], [2, 1], [2, 2]] the answer is 5.

Examples

Example 1

Input:

remove_stones([[0, 0], [0, 1], [1, 0], [1, 2], [2, 1], [2, 2]])

Output:

5

Example 2

Input:

remove_stones([[0, 0], [0, 2], [1, 1], [2, 0], [2, 2]])

Output:

3

Constraints

• 0 <= len(stones) <= 100000
• 0 <= x, y <= 10000
• No two stones share a cell.