Even and Odd Ladders

Hard

You are given two arrays first and second that contain only 0s and 1s. Replace every 0 with a positive **even** number and every 1 with a positive **odd** number. After the replacement both arrays must be strictly increasing, and all numbers across both arrays must be distinct: no number may be used twice, whether in the same array or in different ones. Return the smallest possible value of the largest number that appears in the arrays after the replacement.

Example 1

first=[1, 1], second=[0] → 3

For instance first = [1, 3] and second = [2]: all numbers are distinct, odd ones replace the 1s and the even one replaces the 0. Nothing above 3 is needed.

Example 2

first=[0, 0], second=[0, 0] → 8

Four distinct even numbers are needed; the smallest are 2, 4, 6 and 8, e.g. first = [2, 6] and second = [4, 8].

Example 3

first=[], second=[0, 1, 1] → 5

The first array is empty, and the second becomes [2, 3, 5].

Constraints

0 ≤ len(first) ≤ 1000
1 ≤ len(second) ≤ 1000
first and second contain only 0 and 1

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Topics

Array Dynamic Programming

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Input

first=[1, 1], second=[0]

Expected

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