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> 
#define rint register int
using namespace std;
set<pair<int,int> >st;
int a[222222],flag,n;
inline void pluss(int x,int now)
{
	pair<int,int>tmp;
	if(x<1) flag=-1;
	tmp=*st.lower_bound(make_pair(x,0));
	if(tmp.first!=x) st.insert(make_pair(x,0)),tmp=make_pair(x,0);
	else
	{
		st.erase(tmp);tmp.second++;
		if(tmp.second>=now) pluss(x-1,now);
		else st.insert(tmp);
	}
	while(1)
	{
		if(st.upper_bound(tmp)==st.end()) break;
		tmp=*st.upper_bound(tmp); st.erase(tmp);
	}
}
inline int check(int x)
{
	st.clear(); flag=0;
	for(rint i=1;i<=n;i++) if(a[i]<=a[i-1]) pluss(a[i],x-1);
	if(flag==-1)
		return 0;
	return 1;
}
inline int erf(int l,int r)
{
	while(l<=r)
	{
		int mid=l+r>>1;
		if(check(mid)) r=mid-1;
		else l=mid+1;
	}return l;
}
int main()
{
	cin>>n;int flag=1;
	for(rint i=1;i<=n;i++)
	{
		cin>>a[i];
		flag&=(a[i]>a[i-1]);
	}int ans;
	if(flag==1){cout<<1;return 0;}
	ans=erf(2,n);cout<<ans;
 	return 0;
}
