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;

typedef pair<int,int> pii;
const int N=200010;
int a[N],n,flag;
set<pii> s;

void gao(int x,int now)
{
	pii tmp;
	if(x<1) flag=-1;
	tmp=*s.lower_bound(make_pair(x,0));
	if(tmp.first!=x) s.insert(pii(x,0)),tmp=pii(x,0);
	else
	{
		s.erase(tmp);
		if(++tmp.second>=now) gao(x-1,now);
		else s.insert(tmp);
	}
	while(1)
	{
		if(s.upper_bound(tmp)==s.end()) break;
		tmp=*s.upper_bound(tmp);
		s.erase(tmp);
	}
}

bool check(int x)
{
	s.clear();flag=0;
	for(int i=1;i<=n;i++)
		if(a[i]<=a[i-1]) gao(a[i],x-1);
	return flag!=-1;
}

int main()
{
	int i,flag=1,ans; 
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	{
		scanf("%d",a+i);
		flag&=(a[i]>a[i-1]);
	}
	if(flag) return puts("1"),0;
    int l=2,r=n,mid;
	while(l<=r)
	{
		int mid=l+r>>1;
		if(check(mid)) r=mid-1;
		else l=mid+1;
	}
	printf("%d\n",l); 
 	return 0;
}