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Climb Stairs With Minimum Moves

1. You are given a number n, representing the number of stairs in a staircase. 2. You are on the 0th step and are required to climb to the top. 3. You are given n numbers, where ith element's value represents - till how far from the step you could jump to in a single move. You can of-course fewer number of steps in the move. 4. You are required to print the number of minimum moves in which you can reach the top of staircase. Note -> If there is no path through the staircase print null.

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Climb Stairs With Minimum Moves

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1. You are given a number n, representing the number of stairs in a staircase. 2. You are on the 0th step and are required to climb to the top. 3. You are given n numbers, where ith element's value represents - till how far from the step you could jump to in a single move. You can of-course fewer number of steps in the move. 4. You are required to print the number of minimum moves in which you can reach the top of staircase. Note -> If there is no path through the staircase print null.

Constraints

0 <= n <= 20 0 <= n1, n2, .. <= 20

Format

Input

A number n .. n more elements

Output

A number representing the number of ways to climb the stairs from 0 to top.

Example

Sample Input

10 3 3 0 2 1 2 4 2 0 0

Sample Output

4

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