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;
int main() {
	int n;
	cin>>n;
	vector<long long>a(n);
	for(int i = 0; i < n; i++) {
		cin>>a[i];
	}
	int ok1=1;
	for(int i = 1; i < n; i++) {
		if(a[i]<=a[i-1])ok1=0;
	}
	if(ok1) {
		cout<<1<<endl;
		return 0;
	}
	int s=1,e=n+1;
	while(s+1<e) {
		int m=(s+e)/2;
		int ok=1;
		map<int,int>f;
		int len=0;
		for(int i = 0; i < n; i++) {
			if(a[i]>len) {
				len=a[i];
			} else {
				while(!f.empty() && f.rbegin()->first>=a[i]) {
					f.erase(f.rbegin()->first);
				}
				f[a[i]-1]++;
				int cur=a[i]-1;
				while(f[cur]>=m) {
					f.erase(cur);
					cur--;
					f[cur]++;
					if(cur<0) {
						ok=0;
					}
				}
				if(!ok)break;
				len=a[i];
			}
		}
		if(ok) {
			e=m;
		} else {
			s=m;
		}
	}
	cout<<e<<endl;
	return 0;
}