There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.

At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the minimum possible number of different characters contained in the strings.

Examples

Input

3
3 2 1


Output

2


Input

5
2 3 2 1 2


Output

2
#include <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 1000000007
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3f
#define EPS (1e-10)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

int n;
int a[300000];

bool C(int t){
	map<int,int>mp;
	for(int i=1;i<n;i++){
		if(a[i]>a[i-1])continue;
		int d=a[i];
		while(mp[d]==t){
			if(d==1){
				return false;
			}
			d--;
		}
		mp[d]++;
		auto it=mp.lower_bound(d+1);
		while(it!=mp.end()){
			it=mp.erase(it);
		}
	}
	return true;
}
int main(){
	scanf("%d",&n);
	bool flag=false;
	rep(i,n){
		scanf("%d",&a[i]);
		if(i&&a[i-1]>=a[i])flag=true;
	}
	if(!flag){
		puts("1");return 0;
	}
	int ok=n*2,ng=0;
	while(ok-ng>1){
		int t=(ok+ng)/2;
		if(C(t))ok=t;
		else ng=t;
	}
	cout<<ok+1<<endl;
}
