Fewest Jumps to the End

You stand on the first square of a row. jumps[i] is the longest jump you can make from square i: any distance from 1 up to jumps[i] squares forward. Write min_jumps(jumps) that returns the smallest number of jumps that takes you to the last square.

You can assume the last square can always be reached.

Examples

min_jumps([1, 4, 1, 1, 1, 2])  # returns 2
min_jumps([2, 0, 3, 0, 0, 1])  # returns 2
min_jumps([1, 1, 1, 1])        # returns 3
min_jumps([0])                 # returns 0

In the first example, hop onto the 4 and then jump straight to the last square: two jumps.

Constraints

• 1 <= len(jumps) <= 10000
• 0 <= jumps[i] <= 1000
• The last square is always reachable