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
//Problem C
#include<bits/stdc++.h>
using namespace std;
const int N=200005;
int n,aa[N],x[N],y[N],t,l;
int chk(int v){//printf("chk %d\n",v);
	t=l=0;
	for(int i=1;i<=n;i++){
		int a=aa[i];
		if(a<=l){
			while(t&&a<x[t])--t;int k=a;
			while(t&&x[t]==k&&y[t]==v-1)--t,--k;
			if(!k)return 0;
			if(t&&x[t]==k)++y[t];
			else x[++t]=k,y[t]=1;
		}
		l=a;
		//printf("%d %d  %d",i,a,l);for(int i=1;i<=t;i++)printf(" (%d,%d)",x[i],y[i]);printf("\n");
	}
	return 1;
}
int main(){
	scanf("%d",&n);int f=1;
	for(int i=1;i<=n;i++)scanf("%d",&aa[i]);
	for(int i=1;i<n;i++)if(aa[i]>=aa[i+1])f=0;if(f){printf("1");return 0;}
	int l=2,r=n,s=n;
	while(l<=r){
		int mid=(l+r)>>1;
		if(chk(mid))s=mid,r=mid-1;
		else l=mid+1;
	}
	printf("%d",s);
	return 0;
}