Simplified Hopscotch Game

You are given a game consisting of n cells arranged in a row and numbered from 1 to n. Each cell i has a positive integer written on it, denoted by \(a_i\).

The game is played as follows:

1. The player starts at cell 1.
2. In each move, if the player is currently on cell \(x\), they jump forward exactly \(a_x\) cells, landing on cell \(x + a_x\).
3. If the player lands exactly on cell \(n\), the game ends with a victory.
4. If the player jumps to a cell beyond cell \(n\) (i.e. \(x+a_x > n\)), the player goes out-of-bound and the game ends with a loss.

Your task is to determine:

1. Whether the player wins (i.e. lands exactly on cell \(n\)). Print 1 if the player wins, otherwise 0.
2. The total number of jumps performed by the player.
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inputFormat

The first line of input contains a single integer n (\(1 \leq n \leq 10^5\)), denoting the number of cells.

The second line contains n space-separated positive integers \(a_1, a_2, \ldots, a_n\) where each \(a_i\) represents the number written on the i-th cell.

outputFormat

Output two integers separated by a space. The first integer is 1 if the player wins (i.e. lands exactly on cell \(n\)), or 0 otherwise. The second integer is the total number of jumps performed.

sample

5
3 1 2 1 1

1 2