C. Travelling Salesman Problemtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere are n cities numbered from 1 to n, and city i has beauty a_i.A salesman wants to start at city 1, visit every city exactly once, and return to city 1.For all i\ne j, a flight from city i to city j costs \max(c_i,a_j-a_i) dollars, where c_i is the price floor enforced by city i. Note that there is no absolute value. Find the minimum total cost for the salesman to complete his trip.InputThe first line contains a single integer n (2\le n\le 10^5) — the number of cities.The i-th of the next n lines contains two integers a_i, c_i (0\le a_i,c_i\le 10^9) — the beauty and price floor of the i-th city.OutputOutput a single integer — the minimum total cost.ExamplesInput
3
1 9
2 1
4 1
Output
11
Input
6
4 2
8 4
3 0
2 3
7 1
0 1
Output
13
NoteIn the first test case, we can travel in order 1\to 3\to 2\to 1.   The flight 1\to 3 costs \max(c_1,a_3-a_1)=\max(9,4-1)=9.  The flight 3\to 2 costs \max(c_3, a_2-a_3)=\max(1,2-4)=1.  The flight 2\to 1 costs \max(c_2,a_1-a_2)=\max(1,1-2)=1. The total cost is 11, and we cannot do better.
3
1 9
2 1
4 1

11 
['binary search', 'data structures', 'dp', 'greedy', 'shortest paths', 'sortings', 'two pointers', '*2200']