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>
using namespace std;
int n,l,r,mid,ans;
int a[200005];
struct node{
	int u,l,r;
};

int check(int x){
	stack<node> f;
	f.push((node){1,1,a[1]});
	for(int i=2;i<=n;i++){
		if(a[i]>a[i-1]) f.push((node){1,a[i-1]+1,a[i]});
		else{
			int p;
			while(!f.empty()){
				node v=f.top();
				if(v.l>a[i]) f.pop();
				else{
					p=v.u;f.pop();
					if(v.l<a[i]) f.push((node){p,v.l,a[i]-1});
					break;
				}
			}
			if(p<x) f.push((node){p+1,a[i],a[i]});
			else{
				while(!f.empty()){
					node v=f.top();
					p=v.u;f.pop();
					if(p<x){
						if(v.l!=v.r) f.push((node){p,v.l,v.r-1});
						f.push((node){p+1,v.r,v.r});
						f.push((node){1,v.r+1,a[i]});
						break;
					}
				}
				if(p>=x) return 0;
			}
		}
	}
	return 1;
}

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	l=1,r=1e9,ans=1e9+1;
	while(l<=r){
		mid=(l+r)/2;
		if(check(mid)) ans=min(ans,mid),r=mid-1;
		else l=mid+1;
	}
	printf("%d\n",ans);

	return 0;
}