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<iostream>
#include<map>
using namespace std;
int n;
int a[200001];
map<int,int>m;
bool can(int mid){
	m.clear();
	for(int i=1; i<=n ;i++){
		if(a[i]>a[i-1]) continue;
		auto it=m.end();
		while(!m.empty()){
			--it;
			if(it->first<=a[i]) break;
			m.erase(it);
			it=m.end();
		}
		m[a[i]]++;
		int cur=a[i];
		while(cur>0 && m[cur]==mid){
			m.erase(cur);
			m[--cur]++;
		}
		if(cur==0) return false;
	}
	return true;
}
int main(){
	ios::sync_with_stdio(false);
	cin >> n;
	bool flag=true;
	for(int i=1; i<=n ;i++){
		cin >> a[i];
		if(i>1 && a[i]<=a[i-1]) flag=false;
	}
	if(flag){
		cout << "1\n";
		return 0;
	}
	int l=2,r=3e5,mid;
	while(l!=r){
		mid=(l+r)/2;
		if(can(mid)) r=mid;
		else l=mid+1;
	}
	cout << l << endl;
}