Farmer John's N (1 <= N <= 50,000) cows are standing in a very straight row and mooing. Each cow has a unique height h in the range 1..2,000,000,000 nanometers (FJ really is a stickler for precision). Each cow moos at some volume v in the range 1..10,000. This "moo" travels across the row of cows in both directions (except for the end cows, obviously). Curiously, it is heard only by the closest cow in each direction whose height is strictly larger than that of the mooing cow (so each moo will be heard by 0, 1 or 2 other cows, depending on not whether or taller cows exist to the mooing cow's right or left).

The total moo volume heard by given cow is the sum of all the moo volumes v for all cows whose mooing reaches the cow. Since some (presumably taller) cows might be subjected to a very large moo volume, FJ wants to buy earmuffs for the cow whose hearing is most threatened. Please compute the loudest moo volume heard by any cow.


The input file contains multiple test cases, for each test case:

* Line 1: A single integer, N.

* Lines 2..N+1: Line i+1 contains two space-separated integers, h and v, for the cow standing at location i.

Process till EOF.


For each test case, output:
* Line 1: The loudest moo volume heard by any single cow.

Sample Input

4 2
3 5
6 10

Sample Output



USACO 2006 March