Practice Logic and Mathematics with the exercise "Rocket engines"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

It is a public secret that you need a rocket to go to Mars, but only a few know that your rocket engines must be balanced.
Because Mars is fourth planet from the Sun, your rocket has four engines positioned in matrix 2×2. Before launch, each engine has it own default power, but you as engineer and captain of rocket can change power of engines. In one turn, you can increase by 1 every engine in arbitrary row or column, and you can perform multiple actions (there is no limit).

Imbalance of rocket is defined as difference between maximal engine power and minimal engine power.
Your goal is to find what is the minimal possible imbalance of rocket you can obtain using described action.

Example:
Given default power of each engine:

1 1
0 3

Next actions are performed: 1 × first row, 2 × first column:

1 1 -> 2 2 -> 3 2 -> 4 2
0 3    0 3    1 3    2 3

So minimal imbalance of rocket is 4 - 2 = 2.

Input

Two lines: Matrix 2×2 which represents the default power of each rocket engine.

Output

A single line: Number which represents the minimal imbalance of rocket.

Constraints

a[i][j] - Element of matrix
0 ≤ a[i][j] ≤ 10⁹

Example

Input

1 1
0 3

Output

Solve it

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