LogiQuest

243. Minimum Jumps

MediumGreedyBFS

From index i you may jump up to a[i] steps forward. Print the minimum number of jumps to reach the last index, or -1 if it is impossible.

Input format

Line 1: n Line 2: n non-negative integers

Output format

The minimum jumps, or -1.

Example 1

Input

5
2 3 1 1 4

Output

2

Example 2

Input

5
2 3 0 1 4

Output

2

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 6 test cases, most of them hidden.

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