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Ninja town has ‘N’ houses along a street. The houses are either painted red or blue. The house colours are given in an integer array ‘color’, where 0 denotes the ith house is painted red, and 1 denotes the ith house is painted blue. The residents of a house will be happy if their house colour is different from both its neighbours if they exist. Hence, the Mayor decided to repaint some of the houses. But due to financial reasons, he wants to paint a minimum number of houses. Can you calculate the minimum number of houses that he needs to repaint?

Example: Suppose there are 3 houses and the colours [1, 1, 1], which means all the houses are coloured blue. If the Mayor repaints the second house to red, we will have the colours as [1, 0, 1]. We can see that all the neighbours will be happy. Hence, the minimum number of houses to be repainted is 1.

You have been given a Binary Tree where the value of each node is either 0 or 1. Your task is to return the same Binary Tree but all of its subtrees that don't contain a 1 have been removed.

Note :

A subtree of a node X is X, plus every node that is a descendant of X.

For Example :

Look at the below example to see a Binary Tree pruning.
Input: [1, 1, 1, 0, 1, 0, 1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]

Output: [1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1]

For example, the input for the tree depicted in the below image would be :

1
2 3
4 -1 5 6
-1 7 -1 -1 -1 -1
-1 -1

Explanation :

Level 1 :
The root node of the tree is 1

Level 2 :
Left child of 1 = 2
Right child of 1 = 3

Level 3 :
Left child of 2 = 4
Right child of 2 = null (-1)
Left child of 3 = 5
Right child of 3 = 6

Level 4 :
Left child of 4 = null (-1)
Right child of 4 = 7
Left child of 5 = null (-1)
Right child of 5 = null (-1)
Left child of 6 = null (-1)
Right child of 6 = null (-1)

Level 5 :
Left child of 7 = null (-1)
Right child of 7 = null (-1)

The first not-null node (of the previous level) is treated as the parent of the first two nodes of the current level. The second not-null node (of the previous level) is treated as the parent node for the next two nodes of the current level and so on.
The input ends when all nodes at the last level are null (-1).

Note :

The above format was just to provide clarity on how the input is formed for a given tree.

The sequence will be put together in a single line separated by a single space. Hence, for the above-depicted tree, the input will be given as:
1 2 3 4 -1 5 6 -1 7 -1 -1 -1 -1 -1 -1

We are suffering from the Second wave of Covid-19. The Government is trying to increase its vaccination drives. Ninja wants to help the Government to plan an effective method to help increase vaccination following safety measures. Time is running out. Can you help the nation?

You are given two positive integers: ‘n,’ ‘maxVaccines’ denoting the number of days for which this vaccination drive will go on and the total number of vaccines available for the drive, respectively. You have to find the number of vaccines administered each day. You are also given a number ‘dayNumber,’ and we are interested to know the maximum number of vaccines that can be administered on ‘dayNumber’ th day.

The rules of the vaccination drive :

1. There should be a positive number of vaccines administered each day during the vaccination drive.

2. The absolute difference between the number of vaccines in two consecutive days should not exceed 1.

3. The sum of all the elements of the vaccines array does not exceed maxVaccines, that is, you cannot administer more vaccines than what is provided to you.

4. Vaccines administered on ‘dayNumber’ th day should be maximized.