Codeforces Round #228 (Div. 2) C. Fox and Box Accumulation

C. Fox and Box Accumulation

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Fox Ciel has n boxes in her room. They have the same size and weight, but they might have different strength. The i-th box can hold at most xi boxes on its top (we'll call xi the strength of the box).

Since all the boxes have the same size, Ciel cannot put more than one box directly on the top of some box. For example, imagine Ciel has three boxes: the first has strength 2, the second has strength 1 and the third has strength 1. She cannot put the second and the third box simultaneously directly on the top of the first one. But she can put the second box directly on the top of the first one, and then the third box directly on the top of the second one. We will call such a construction of boxes a pile.

Fox Ciel wants to construct piles from all the boxes. Each pile will contain some boxes from top to bottom, and there cannot be more than xi boxes on the top of i-th box. What is the minimal number of piles she needs to construct?

Input

The first line contains an integer n (1 ≤ n ≤ 100). The next line contains n integers x1, x2, ..., xn (0 ≤ xi ≤ 100).

Output

Output a single integer — the minimal possible number of piles.

Examples

input

3
0 0 10

output

2

input

5
0 1 2 3 4

output

1

input

4
0 0 0 0

output

4

input

9
0 1 0 2 0 1 1 2 10

output

3

这题的贪心得逆向考虑，就是从小到大贪心，先看小的 a[i]值，看后面有没有能承受住这个箱子的其他箱子，如果有那么叠加箱子的数量，接着找。

/* ***********************************************
Author        :guanjun
Created Time  :2016/8/10 22:51:00
File Name     :cf228c.cpp
************************************************ */
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <iomanip>
#include <list>
#include <deque>
#include <stack>
#define ull unsigned long long
#define ll long long
#define mod 90001
#define INF 0x3f3f3f3f
#define maxn 10010
#define cle(a) memset(a,0,sizeof(a))
const ull inf = 1LL << 61;
const double eps=1e-5;
using namespace std;
priority_queue<int,vector<int>,greater<int> >pq;
struct Node{
    int x,y;
};
struct cmp{
    bool operator()(Node a,Node b){
        if(a.x==b.x) return a.y> b.y;
        return a.x>b.x;
    }
};

bool cmp(int a,int b){
    return a>b;
}
int a[maxn];
int vis[maxn];
int main()
{
    #ifndef ONLINE_JUDGE
    //freopen("in.txt","r",stdin);
    #endif
    //freopen("out.txt","w",stdout);
    int n;
    cle(vis);
    cin>>n;
    for(int i=1;i<=n;i++)cin>>a[i];
    sort(a+1,a+1+n);
    int ans=0;
    for(int i=1;i<=n;i++){
        if(!vis[i]){
            int num=1;
            for(int j=i+1;j<=n;j++){
                if(a[j]>=num&&!vis[j]){
                    num++;vis[j]=1;
                }
            }
            ans++;
        }
    }
    cout<<ans<<endl;
    return 0;
}