1840 - Maximum Building Height\.

Hard

You want to build n new buildings in a city. The new buildings will be built in a line and are labeled from 1 to n.

However, there are city restrictions on the heights of the new buildings:

• The height of each building must be a non-negative integer.

• The height of the first building must be 0.

• The height difference between any two adjacent buildings cannot exceed 1.

Additionally, there are city restrictions on the maximum height of specific buildings. These restrictions are given as a 2D integer array restrictions where <code>restrictionsi = id_i, maxHeight_i</code> indicates that building <code>id_i</code> must have a height less than or equal to <code>maxHeight_i</code>.

It is guaranteed that each building will appear at most once in restrictions, and building 1 will not be in restrictions.

Return the maximum possible height of the tallest building.

Example 1:

Input: n = 5, restrictions = \[\[2,1],4,1]

Output: 2

Explanation: The green area in the image indicates the maximum allowed height for each building. We can build the buildings with heights 0,1,2,1,2, and the tallest building has a height of 2.

Example 2:

Input: n = 6, restrictions = []

Output: 5

Explanation: The green area in the image indicates the maximum allowed height for each building. We can build the buildings with heights 0,1,2,3,4,5, and the tallest building has a height of 5.

Example 3:

Input: n = 10, restrictions = \[\[5,3],2,5,7,4,10,3]

Output: 5

Explanation: The green area in the image indicates the maximum allowed height for each building. We can build the buildings with heights 0,1,2,3,3,4,4,5,4,3, and the tallest building has a height of 5.

Constraints:

• <code>2 <= n <= 10⁹</code>

• <code>0 <= restrictions.length <= min(n - 1, 10⁵)</code>

• <code>2 <= id_i<= n</code>

• <code>id_i</code> is unique.

• <code>0 <= maxHeight_i<= 10⁹</code>