Beautiful String

A binary string is a string which contains only "0" and "1".

A substring of the string is a string that can be obtained by deleting some number of characters from the start and/or end.

Sakurako considers a binary string beautiful if the number of ones is at least $2$ and this number divides the length of the string.

For example, "1001", "011100" and "010100100" are beautiful strings, but strings "101", "01010" and "1001000" are not beautiful.

Sakurako loves beautiful strings, but she is bad at searching for them. So, she asks you to help her find any beautiful substring of the given string.

Input

The first line contains one integer $n$ ($3\le n\le 2\cdot 10^5$) — the length of the string.

The second line contains one binary string — the string where Sakurako lost her beautiful string.

It is guaranteed that there are at least three characters "1" in the string.

It is possible to show that the answer always exists.

Output

Output two integers $l$ and $r$ ($1\le l\le r\le n$) where the substring starting at $l$ and ending at $r$ is beautiful. If there are multiple solutions, output any.

Examples

Note

In the first example, the substring "1010" is beautiful since the length, which is $4$, is divisible by the number of ones, which is $2$.

In the second example, the substring "11" is beautiful since the length, which is $2$, is divisible by the number of ones, which is $2$.

Scoring

You will receive at least $32$ points if your solution works correctly for $n\le 1000$.