C. Deep Down Belowtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputIn a certain video game, the player controls a hero characterized by a single integer value: power. The hero will have to beat monsters that are also characterized by a single integer value: armor.On the current level, the hero is facing n caves. To pass the level, the hero must enter all the caves in some order, each cave exactly once, and exit every cave safe and sound. When the hero enters cave i, he will have to fight k_i monsters in a row: first a monster with armor a_{i, 1}, then a monster with armor a_{i, 2} and so on, finally, a monster with armor a_{i, k_i}.The hero can beat a monster if and only if the hero's power is strictly greater than the monster's armor. If the hero can't beat the monster he's fighting, the game ends and the player loses. Note that once the hero enters a cave, he can't exit it before he fights all the monsters in it, strictly in the given order.Each time the hero beats a monster, the hero's power increases by 1.Find the smallest possible power the hero must start the level with to be able to enter all the caves in some order and beat all the monsters.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 10^5). Description of the test cases follows.The first line of each test case contains a single integer n (1 \le n \le 10^5) — the number of caves.The i-th of the next n lines contains an integer k_i (1 \le k_i \le 10^5) — the number of monsters in the i-th cave, followed by k_i integers a_{i, 1}, a_{i, 2}, \ldots, a_{i, k_i} (1 \le a_{i, j} \le 10^9) — armor levels of the monsters in cave i in order the hero has to fight them.It is guaranteed that the sum of k_i over all test cases does not exceed 10^5.OutputFor each test case print a single integer — the smallest possible power the hero must start the level with to be able to enter all the caves in some order and beat all the monsters.ExampleInput
2
1
1 42
2
3 10 15 8
2 12 11
Output
43
13
NoteIn the first test case, the hero has to beat a single monster with armor 42, it's enough to have power 43 to achieve that.In the second test case, the hero can pass the level with initial power 13 as follows:   enter cave 2:   beat a monster with armor 12, power increases to 14;  beat a monster with armor 11, power increases to 15;   enter cave 1:   beat a monster with armor 10, power increases to 16;  beat a monster with armor 15, power increases to 17;  beat a monster with armor 8, power increases to 18.  
2
1
1 42
2
3 10 15 8
2 12 11

43 13 
['binary search', 'greedy', 'sortings', '*1300']