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<cstring>
using namespace std;
const int N=2e5+100;
int a[N],d[N],f[N];
int main()
{
	int n;scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	int l=1,r=n,ans;
	while(l<=r){
		int mid=(l+r)>>1;
		d[0]=0;
		bool pd=true;
		for(int i=1;i<=n;i++){
			if(a[i]<=a[i-1]){
				while(d[0]&&d[d[0]]>a[i]) d[0]--;
				if(d[d[0]]!=a[i]) d[++d[0]]=a[i],f[d[0]]=0;
				f[d[0]]++;
				while(f[d[0]]==mid){
					if(d[d[0]]==1) {pd=false;break;}
					d[0]--;
					int t=d[d[0]+1]-1;
					if(d[d[0]]!=t) d[++d[0]]=t,f[d[0]]=0;
					f[d[0]]++; 
				}
				if(!pd) break;
			}
		}
		if(pd) ans=mid,r=mid-1;
		else l=mid+1;
	}
	printf("%d\n",ans);
	return 0;
}