oql has some beads of the forms 00, 01, and 11. As a craft enthusiast, oql wants to string them into a bracelet and has carefully designed the pattern and drawn a blueprint.

The pattern of the bracelet can be abstracted as a string $S$ consisting of 0 and 1, where the ends are connected.

However, a cat named Iris passed by, and now there are only $n$, $m$, and $k$ beads of the three types remaining, respectively.

oql is very sad, but still decides to try his best to complete the bracelet, or at least a continuous part of it. He wants to know the maximum length of a continuous part he can complete now.

Obviously, you should not break the beads. However, you can flip the beads: for 00 and 11, there is no change after flipping; for 01, it becomes 10 after flipping.

Input

The first line contains three space-separated integers $n, m, k$ ($0 \le n, m, k \le 10^6$), representing the number of 00, 01, and 11 beads, respectively.

The second line contains a string $S$ consisting of 0 and 1 ($1 \le |S| \le 10^6$), representing the pattern of the bracelet.

Output

A single integer representing the maximum length oql can complete.

Examples

Input 1

0 2 3
01001111

Output 1

6

Input 2

1 2 3
0

Output 2

0

Input 3

1 1 3
0101000011

Output 3

6