First and Last Nonzero Positions (Vị trí số khác 0 đầu tiên và cuối cùng)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given $a_0,\ldots,a_{n-1}$, define

If $I$ is nonempty, print $L=\min I$ and $R=\max I$. If $I$ is empty, print -1 -1. Indices are 0-based.

Input

The first line contains $n$. The second line contains $n$ integers $a_i$.

Output

Print L R as defined.

Subtask

Subtask 1 (20 points): $1\le n\le10$, $|a_i|\le10^3$.

Subtask 2 (30 points): $1\le n\le5000$, $|a_i|\le10^6$.

Subtask 3 (50 points): $1\le n\le2\cdot10^5$, $|a_i|\le10^9$.

Example

Input

7
0 0 5 0 -2 0 0

Output

2 4

Explanation

The sample follows the definitions and rules above.