Minimums and Maximums

2000ms

524288K

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:

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:

For each test case, print one integer — the minimum possible number of elements in a beautiful array.

Sample Input:

Sample Output:

Note:

Optimal arrays in the test cases of the example:

$$$[1, 1, 1, 1]$$$, it has $$$4$$$ minimums and $$$4$$$ maximums;
$$$[4, 4, 4, 4, 4]$$$, it has $$$5$$$ minimums and $$$5$$$ maximums;
$$$[1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2]$$$, it has $$$3$$$ minimums and $$$10$$$ maximums;
$$$[8, 8, 8]$$$, it has $$$3$$$ minimums and $$$3$$$ maximums;
$$$[4, 6, 6]$$$, it has $$$1$$$ minimum and $$$2$$$ maximums;
$$$[3, 4, 3]$$$, it has $$$2$$$ minimums and $$$1$$$ maximum;
$$$[5, 5, 5, 5, 5, 5]$$$, it has $$$6$$$ minimums and $$$6$$$ maximums.

Informação

Provedor Codeforces

Código CF1680A