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 arr[200003] , N; vector < int > pot;

#define PII pair < int , int >
PII stk[200003]; int top;
bool check(int mid){
	top = 0;
	for(auto t : pot){
		while(top && stk[top].first > t) --top;
		auto add = [&](int x){
			if(top && stk[top].first == x) ++stk[top].second;
			else stk[++top] = PII(x , 1);
		};
		add(t);
		while(stk[top].first && stk[top].second == mid){--top; add(stk[top + 1].first - 1);}
		if(stk[top].first == 0) return 0;
	}
	return 1;
}

int main(){
	ios::sync_with_stdio(0); cin >> N;
	for(int i = 1 ; i <= N ; ++i) cin >> arr[i];
	for(int i = 2 ; i <= N ; ++i) if(arr[i] <= arr[i - 1]) pot.push_back(arr[i]);
	int L = 1 , R = N + 1;
	while(L < R){int mid = (L + R) >> 1; check(mid) ? R = mid : L = mid + 1;}
	cout << L; return 0;
}