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<iostream>
#include<string.h>
#include<stdio.h>
#include<math.h>
#define eps 1e-7
#define N 1200000
using namespace std;
int a[N],n;
int q[N],b[N];
bool check(int x){
	int tail=0;
	for(int i=1;i<=n;i++){
		int o=a[i];
		if(o>q[tail]){
			q[++tail]=o;
			b[tail]=1;
			continue;
		}
		if(x==1)return 0;
		while(tail>0&&q[tail]>o)tail--;
		while(tail>0&&q[tail]==o&&b[tail]==x)tail--,o--; 
		if(tail==0&&o==0)return 0;
		if(q[tail]==o)b[tail]++;
		else q[++tail]=o,b[tail]=2;
		
	}
	return 1;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	int l=1,r=n;
	check(2);
	while(r-l>3){
		int mid=(l+r)/2;
		if(check(mid))r=mid;
		else l=mid+1;
	}
	check(2);
	for(int i=l;i<=r;i++){
		if(check(i)){
			printf("%d\n",i);
			return 0;
		}
	}
}