Rocket engines
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 1Next actions are performed: 1 × first row, 2 × first column:
0 3
1 1 -> 2 2 -> 3 2 -> 4 2So minimal imbalance of rocket is 4 - 2 = 2.
0 3 0 3 1 3 2 3
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
0 ≤ a[i][j] ≤ 10⁹
Example
Input
1 1 0 3
Output
2
Tags
Mathematics, Logic
Difficulty
Medium
Test cases
Test 1 Test
Input
1 1
0 3
Output
2
Validator 1 Validator
Input
9 8
7 0
Output
3
Test 2 Test
Input
6 6
6 6
Output
0
Validator 2 Validator
Input
0 0
0 0
Output
0
Test 3 Test
Input
3 12
12 3
Output
9
Validator 3 Validator
Input
7 19
7 18
Output
1
Test 4 Test
Input
83 104
84 64
Output
21
Validator 4 Validator
Input
81 6
106 89
Output
29
Test 5 Test
Input
1120 1193
1185 1096
Output
81
Validator 5 Validator
Input
640 520
640 382
Output
69
Test 6 Test
Input
2593648 2164630
3695065 5851421
Output
1292687
Validator 6 Validator
Input
1973577 6675192
9961385 3042054
Output
5810473
Test 7 Test
Input
466643937 459483554
462812334 456924340
Output
636195
Validator 7 Validator
Input
236663937 161103138
151141275 103777855
Output
14098690
Test 8 Test
Input
257096859 257096859
45867751 257096859
Output
105614554
Validator 8 Validator
Input
329249334 363706684
341679234 39992214
Output
168072185
Test 9 Test
Input
32095790 173465731
71866326 424205669
Output
105484701
Validator 9 Validator
Input
225352867 225352867
460683533 225352867
Output
117665333
Test 10 Test
Input
208949331 489817533
208949331 489817533
Output
0
Validator 10 Validator
Input
467765325 497519746
60981056 2717947
Output
44008765
Solution language
Solution
Stub generator input