F7 Championship Candidates

Only the final race of the prestigious F7 racing tournament remains. F7 is popular because the drivers' rankings often change from race to race. Sanggeun is a huge fan of F7, but the final race conflicts with his midterm exam, so he cannot attend.

All races except the final one have already finished. The final champion of F7 is any driver whose total score over all races is maximum. If several drivers share the maximum total score, all of them are champions.

In the final race, the 1st-place driver earns N points, the 2nd-place driver earns N-1 points, ..., and the last-place driver earns 1 point. No two drivers have the same rank in a race.

Given each driver's score immediately before the final race, determine how many drivers can become a champion for at least one possible final-race ranking.

The first line contains the number of drivers N participating in F7. (3 ≤ N ≤ 300,000)

Each of the next N lines contains B_i, the score earned by one driver before the final race. (0 ≤ B_i ≤ 2,000,000, i = 1, ..., N)

Print the number of drivers who can possibly become a champion.