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Thursday 4 August 2022

[Solution] Robot in a Hallway Codeforces Solution



C. Robot in a Hallway
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There is a grid, consisting of 2 rows and m columns. The rows are numbered from 1 to 2 from top to bottom. The columns are numbered from 1 to m from left to right.

The robot starts in a cell (1,1). In one second, it can perform either of two actions:

  • move into a cell adjacent by a side: up, right, down or left;
  • remain in the same cell.

The robot is not allowed to move outside the grid.

Initially, all cells, except for the cell (1,1), are locked. Each cell (i,j) contains a value ai,j — the moment that this cell gets unlocked. The robot can only move into a cell (i,j) if at least ai,j seconds have passed before the move.

The robot should visit all cells without entering any cell twice or more (cell (1,1) is considered entered at the start). It can finish in any cell.

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 occupied

What is the fastest the robot can achieve that?

Input

The first line contains a single integer t (1t104) — the number of testcases.

The first line of each testcase contains a single integer m (2m2105) — the number of columns of the grid.

The i-th of the next 2 lines contains m integers ai,1,ai,2,,ai,m (0ai,j109) — the moment of time each cell gets unlocked. a1,1=0. If ai,j=0, then cell (i,j) is unlocked from the start.

The sum of m over all testcases doesn't exceed 2105.

Output

For each testcase, print a single integer — the minimum amount of seconds that the robot can take to visit all cells without entering any cell twice or more.

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