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문제

Yuuka has a deck of $n$ cards labeled with $0, 1, 2, \dots, (n - 1)$.

Initially, the cards are placed in the order $p_1, p_2, \dots, p_n$ from top to bottom. In each round, if the top card is labeled with $x$, Yuuka will place it $x$ cards downward, so it becomes the card number $(x + 1)$ in the deck, counting from $1$. The relative order of other cards will not be changed.

How many rounds will pass until the card labeled with $0$ comes to the top?

입력

The first line contains an integer $n$ ($1 \leq n \leq 32$).

The second line contains $n$ distinct integers $p_1, p_2, \dots, p_n$ ($0 \leq p_i < n$).

출력

Output an integer which denotes the number of rounds. If the card labeled with $0$ never comes to the top, output "-1" instead.

예제 입력 1

5
1 3 2 4 0

예제 출력 1

13

예제 입력 2

2
0 1

예제 출력 2

0