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 maxn = 234566;
int a[maxn], n;
bool check(int m){
	struct interval { int l, r, v; };
	vector<interval> in;
       	in.push_back({0, a[0], 0});
	for(int i = 1; i < n; i++){
		if(a[i] > a[i - 1]){
			in.push_back({a[i - 1], a[i], 0});
			continue;
		}
		while(!in.empty() && in.back().l >= a[i]) in.pop_back();
	       	in.back().r = a[i];	
		while(!in.empty() && in.back().v == m - 1) in.pop_back();
		if(in.empty()) return false;
		interval cur = in.back(); in.pop_back();
		if(cur.l != cur.r - 1) in.push_back({cur.l, cur.r - 1, cur.v});
		in.push_back({cur.r - 1, cur.r, cur.v + 1});
	    	if(cur.r != a[i]) in.push_back({cur.r, a[i], 0});
	}
	return true;
}
int main(){
	cin >> n;
	for(int i = 0; i < n; i++) cin >> a[i];
	int lo = 1, hi = 3 * n, ans = 0;
	while(lo <= hi){
		int mid = (lo + hi)>>1;
		if(check(mid)) hi = mid - 1, ans = mid;
		else lo = mid + 1;
	}
	return !printf("%d\n", ans);
}
