474. Ones and Zeroes

Difficulty: Medium

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Problem

You are given an array of binary strings strs and two integers m and n.

Return the size of the largest subset of strs such that there are at most m 0's and n 1's in the subset.

A set x is a subset of a set y if all elements of x are also elements of y.

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Examples

Example 1

Input

strs = ["10","0001","111001","1","0"], m = 5, n = 3

Output

4

Explanation

The largest subset with at most 5 0's and 3 1's is {"10", "0001", "1", "0"}, so the answer is 4.

Other valid but smaller subsets include {"0001", "1"} and {"10", "1", "0"}.

{"111001"} is an invalid subset because it contains 4 1's, greater than the maximum of 3.

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Example 2

Input

strs = ["10","0","1"], m = 1, n = 1

Output

2

Explanation

The largest subset is {"0", "1"}, so the answer is 2.

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Constraints

1 <= strs.length <= 600
1 <= strs[i].length <= 100
strs[i] consists only of digits '0' and '1'
1 <= m, n <= 100