CF1680A Minimums and Maximums
Description
An array is beautiful if both of the following two conditions meet:
- there are at least $ l_1 $ and at most $ r_1 $ elements in the array equal to its minimum;
- there are at least $ l_2 $ and at most $ r_2 $ elements in the array equal to its maximum.
For example, the array $ [2, 3, 2, 4, 4, 3, 2] $ has $ 3 $ elements equal to its minimum ( $ 1 $ -st, $ 3 $ -rd and $ 7 $ -th) and $ 2 $ elements equal to its maximum ( $ 4 $ -th and $ 5 $ -th).
Another example: the array $ [42, 42, 42] $ has $ 3 $ elements equal to its minimum and $ 3 $ elements equal to its maximum.
Your task is to calculate the minimum possible number of elements in a beautiful array.
Input Format
The first line contains one integer $ t $ ( $ 1 \le t \le 5000 $ ) — the number of test cases.
Each test case consists of one line containing four integers $ l_1 $ , $ r_1 $ , $ l_2 $ and $ r_2 $ ( $ 1 \le l_1 \le r_1 \le 50 $ ; $ 1 \le l_2 \le r_2 \le 50 $ ).
Output Format
For each test case, print one integer — the minimum possible number of elements in a beautiful array.
Explanation/Hint
Optimal arrays in the test cases of the example:
1. $ [1, 1, 1, 1] $ , it has $ 4 $ minimums and $ 4 $ maximums;
2. $ [4, 4, 4, 4, 4] $ , it has $ 5 $ minimums and $ 5 $ maximums;
3. $ [1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2] $ , it has $ 3 $ minimums and $ 10 $ maximums;
4. $ [8, 8, 8] $ , it has $ 3 $ minimums and $ 3 $ maximums;
5. $ [4, 6, 6] $ , it has $ 1 $ minimum and $ 2 $ maximums;
6. $ [3, 4, 3] $ , it has $ 2 $ minimums and $ 1 $ maximum;
7. $ [5, 5, 5, 5, 5, 5] $ , it has $ 6 $ minimums and $ 6 $ maximums.