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<cstdio>
using namespace std;
int n,top;
const int N=200010;
int len[N];
struct wei{int pos,val;}zhan[N];
void Insert(int l,int mid)
{
	while(zhan[top].pos>l)--top;
	if(zhan[top].pos==l)++zhan[top].val;
	else zhan[++top]=(wei){l,1};
	if(top>1&&zhan[top].val==mid)--top,Insert(l-1,mid);
}
int check(int mid)
{
	zhan[top=1]=(wei){0,0};
	for(int i=2;i<=n;++i)
		if(len[i]<=len[i-1])Insert(len[i],mid);
	return zhan[1].val==0;
}
int pan(){for(int i=2;i<=n;++i)if(len[i]<=len[i-1])return 0;return 1;}
int main()
{
	cin>>n;
	for(int i=1;i<=n;++i)scanf("%d",&len[i]);
	if(pan())return puts("1")==2333;
	int l=2,r=n,mid,ans=1;
	while(l<=r)
	{
		mid=(l+r)>>1;
		if(check(mid))ans=mid,r=mid-1;
		else l=mid+1;
	}
	cout<<ans;
	return 0;
}