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<cstdio>
#include<map>
using namespace std;
#define N 215000
map<int,int> tp;
int n,s[N];
bool check(int k)
{
	if(k==1){for(int i=2;i<=n;i++)if(s[i]<=s[i-1])return 0;return 1;}
	tp.clear();
	int ls=0;
	for(int i=1;i<=n;i++)
	{
		if(s[i]>ls){ls=s[i];continue;}
		while(1)
		{
			if(!tp.size())break;
			map<int,int>::reverse_iterator it=tp.rbegin();
			if(it->first<=s[i])break;
			tp.erase(--(it.base()));
		}
		tp[s[i]]++;
		int t=s[i];
		while(tp[t]>=k){if(t==1)return 0;tp[t]-=k,tp[t-1]++,t--;}
		ls=s[i];
	}
	return 1;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&s[i]);
	int lb=1,rb=n,as=n;
	while(lb<=rb)
	{
		int mid=(lb+rb)>>1;
		if(check(mid))as=mid,rb=mid-1;
		else lb=mid+1;
	}
	printf("%d\n",as);
}//