2018年3月USACO美国计算机奥赛Open Contest公开赛银级题2

USACO 2018 US Open Contest, Silver Problem 2. Lemonade Line

2018年3月USACO美国计算机奥赛公开赛银级题2

It’s a hot summer day out on the farm, and Farmer John is serving lemonade to his NN cows! All NN cows (conveniently numbered 1N1…N) like lemonade, but some of them like it more than others. In particular, cow ii is willing to wait in a line behind at most wiwicows to get her lemonade. Right now all NN cows are in the fields, but as soon as Farmer John rings his cowbell, the cows will immediately descend upon FJ’s lemonade stand. They will all arrive before he starts serving lemonade, but no two cows will arrive at the same time. Furthermore, when cow ii arrives, she will join the line if and only if there are at most wiwi cows already in line.

Farmer John wants to prepare some amount of lemonade in advance, but he does not want to be wasteful. The number of cows who join the line might depend on the order in which they arrive. Help him find the minimum possible number of cows who join the line.

INPUT FORMAT (file lemonade.in):

The first line contains NN, and the second line contains the NN space-separated integers w1,w2,,wNw1,w2,…,wN. It is guaranteed that 1N1051≤N≤105, and that 0wi1090≤wi≤109 for each cow ii.

OUTPUT FORMAT (file lemonade.out):

Print the minimum possible number of cows who might join the line, among all possible orders in which the cows might arrive.

SAMPLE INPUT:

5
7 1 400 2 2

SAMPLE OUTPUT:

3

In this setting, only three cows might end up in line (and this is the smallest possible). Suppose the cows with w=7w=7 and w=400w=400arrive first and wait in line. Then the cow with w=1w=1 arrives and turns away, since 2 cows are already in line. The cows with w=2w=2then arrive, one staying and one turning away.