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;
typedef long long LL;

int main(){
	int n;
	cin >> n;
	vector<LL> 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 << '\n';
		return 0;
	}

	int s = 1; // can't
	int e = n + 1; // can

	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 << '\n';
}