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;
const int N=200005;
int n,a[N],ans,f=0;
map <int,int> mp;
bool check(int x){
	mp.clear();
	for (int i=2;i<=n;i++)
		if (a[i-1]>=a[i]){
			while (!mp.empty()){
				int t=mp.rbegin()->first;
				if (t>a[i]) mp.erase(t); 
				else break;
			}
			int j=a[i];
			while (mp[j]+1==x) mp.erase(j),j--;
			if (j==0) return false;
			mp[j]++;
		}
	return true;
}
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++) {
		scanf("%d",&a[i]);
		if (a[i]<=a[i-1]) f=1;
	}
	if (!f) {puts("1");return 0;}
	int l=2,r=n;
	while (l<=r){
		int mid=(l+r)>>1;
		if (check(mid)){
			ans=mid;
			r=mid-1;
		}else l=mid+1;
	}
	printf("%d\n",ans);
}