Problem Description

JOI-kun found a sugoroku board at his uncle's house. The sugoroku board consists of $ N+2 $ squares arranged in a straight line, with the $ 1 $st square being the start and the $ N+2 $nd square being the goal. Each of the other squares contains either $ 0 $ or $ 1 $, and for each $ i $ ($1 \leq i \leq N$), the number written on the $ i+1 $th square is $ A_i $.

In sugoroku, you initially place a piece on the start square and repeatedly roll a die to move the piece forward by the number of spaces shown on the die. However, if the piece lands on a square with a $ 1 $, the game is over. If you can stop on the goal square or pass it without landing on a $ 1 $, you clear the game.

JOI-kun decided to go to the toy store to buy a die to play the sugoroku. The toy store sells $ N+1 $ dice. The $ j $th die ($1 \leq j \leq N+1$) has $ j $ faces, each showing numbers $ 1, 2, ..., j $.

JOI-kun decided to buy the die with the fewest faces that allows him to clear the game. Which die should JOI-kun buy?

Input Format

The input is given from the standard input in the following format:

$ N $ $ A_1 $ $ A_2 $ ... $ A_N $

Output Format

Output the number of faces of the die that JOI-kun should purchase.

Sample Input and Output

Sample Input #1

5
0 1 0 0 0

Sample Output #1

2

Sample Input #2

5
1 1 1 1 1

Sample Output #2

6

Sample Input #3

7
0 0 1 0 1 1 0

Sample Output #3

3

Notes/Hints

Constraints

• $1 \leq N \leq 100$
• $0 \leq A_i \leq 1$ ($1 \leq i \leq N$)

Sample Explanation 1

The sugoroku consists of $ 7 $ squares, with only the $ 3 $rd square containing a $ 1 $. If you use a die with $ 2 $ faces, for example, if the rolls are $ 1, 2, 1, 1, 1 $, you can clear the game. This is the minimum, so output $ 2 $.

Sample Explanation 2

The sugoroku consists of $ 7 $ squares, with all squares except the start and goal containing a $ 1 $. In this case, a die with $ 6 $ faces is necessary. This is the minimum, so output $ 6 $.

见题面 Input 部分

见题面 Output 部分