You are playing a game of tag with your friends. In tag, people are divided into two teams: people who are "it", and people who are not "it". The people who are "it" want to catch as many people as possible who are not "it".

You are given a 0-indexed integer array team containing only zeros (denoting people who are not "it") and ones (denoting people who are "it"), and an integer dist. A person who is "it" at index i can catch any one person whose index is in the range [i - dist, i + dist] (inclusive) and is not "it".

Return the maximum number of people that the people who are "it" can catch.

 

Example 1:

Input: team = [0,1,0,1,0], dist = 3
Output: 2
Explanation:
The person who is "it" at index 1 can catch people in the range [i-dist, i+dist] = [1-3, 1+3] = [-2, 4].
They can catch the person who is not "it" at index 2.
The person who is "it" at index 3 can catch people in the range [i-dist, i+dist] = [3-3, 3+3] = [0, 6].
They can catch the person who is not "it" at index 0.
The person who is not "it" at index 4 will not be caught because the people at indices 1 and 3 are already catching one person.

Example 2:

Input: team = [1], dist = 1
Output: 0
Explanation:
There are no people who are not "it" to catch.

Example 3:

Input: team = [0], dist = 1
Output: 0
Explanation:
There are no people who are "it" to catch people.

 

Constraints:

• 1 <= team.length <= 105
• 0 <= team[i] <= 1
• 1 <= dist <= team.length