Solve the programming task below in a Python markdown code block.
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.


-----Examples-----

Input
7
3 5 4 6
5 8 5 5
3 3 10 12
1 5 3 3
1 1 2 2
2 2 1 1
6 6 6 6
Output
4
5
13
3
3
3
6


-----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.