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>
const int N=2e5+5;
struct seg{int l,r,c;}st[N*2];
int n,a[N],w,l,r,m,i;
int main(){
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%d",a+i);
	for(l=1,r=n;l<r;){
		m=l+r>>1;st[w=1]=(seg){1,a[1],1};
		for(i=2;i<=n;++i)if(a[i]>a[i-1])st[++w]=(seg){a[i-1]+1,a[i],1};else{
			for(;w && st[w].l>a[i];--w);
			st[w].r=a[i];
			for(;w && st[w].c==m;--w);
			if(!w)break;
			if(st[w].l==st[w].r)++st[w].c;else st[w+1]=(seg){st[w].r,st[w].r,st[w].c+1},--st[w].r,++w;
			if(st[w].r<a[i])st[w+1]=(seg){st[w].r+1,a[i],1},++w;
		}
		if(i<=n)l=m+1;else r=m;
	}
	printf("%d\n",l);
	return 0;
}