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 re register
#define ui unsigned int
#define ull unsigned long long
int a[200100],f[200100],q[200100],nm[200100],ta,n;
bool check(re int mid)
{
	ta=0;
	for(re int i=2;i<=n;i++)if(a[i]<=a[i-1])
	{
		if(mid==0)return 0;
		while(q[ta]>a[i])ta--;
		re int x=a[i];
		for(;x;x--)
		{
			if(!ta||q[ta]!=x){q[++ta]=x,nm[ta]=1;break;}
			else if(nm[ta]<mid){nm[ta]++;break;}
			else ta--;
		}
		//printf("***%d %d %d\n",i,x,ta);
		if(!x)return 0;
	}
	return 1;
}
int main()
{
	scanf("%d",&n);
	f[0]=1e9;
	for(re int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
	}
	re int l=0,r=n,mid;
	for(mid=(l+r)/2;l<r;mid=(l+r)/2)
	{
		//printf("**%d %d %d\n",l,r,mid);
		if(check(mid))r=mid;else l=mid+1;
	}
	printf("%d\n",l+1);
}