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## Win After Last Round Solution

You are given a list of integers nums of length n representing the current score of swimmers in a competition. There is one more round to swim and the first place winner for this round gets n points, second place n-1 points, etc. and the last place gets 1 point.

Return the number of swimmers that can still win the competition after the last round. If you tie for first in points, this still counts as winning.

Constraints

n ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [8, 7, 10, 11]

Output

3

Explanation

The swimmers that currently have 8, 10 and 11 points can all win if final score is [12, 10, 12, 12]. That is, the 8 point swimmer gets first place, 7 point swimmer swimmer gets second, 10 point swimmer gets third, and 11 point swimmer gets last place.

Even if the 7 point swimmer gets first place and has final score of 11 points, 8 point swimmer gets second, the third place person would still get 2 points so the last two swimmers would still get at least 12 points. So the 7 point swimmer cannot win the competition.