A Seat Far From Everyone

Medium

A row of seats in a hall is described by the array row: row[i] = 1 if seat i is taken and 0 if it is free. The row has at least one free seat and at least one taken seat. You want to take a free seat so that the distance to your nearest neighbour is as large as possible. The distance between seats i and j is |i - j|. Return that largest possible distance.

Example 1

row=[1, 0, 0, 0, 0, 0, 1, 0, 1] → 3

Taking seat 3 leaves the nearest neighbour 3 seats away on both sides. Nothing does better.

Example 2

row=[0, 0, 0, 0, 1, 1] → 4

The best choice is the very end, seat 0: the nearest person is 4 seats away.

Example 3

row=[1, 0] → 1

Constraints

2 ≤ len(row) ≤ 10⁵
row[i] is 0 or 1
At least one seat is free and at least one is taken

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Topics

Array

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Input

row=[1, 0, 0, 0, 0, 0, 1, 0, 1]

Expected

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