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<stack>
using namespace std;
int main() {
	static int N, A[200000];
	cin >> N;
	for (int i = 0;i < N;++ i) cin >> A[i];
	int ans = 0, max = N, mid, halfDiff, tmp;
	while(halfDiff = max - ans >> 1) { // 二分探索
		bool check = false;
		mid = ans + halfDiff;
		stack<pair<int, int> > stk;
		for (int j = 1;j < N;++ j) { // シミュレーション
			if (A[j - 1] >= A[j]) { // 文字数が減るパターン
				while (!stk.empty() && stk.top().first > A[j]) stk.pop();
				if (stk.empty() || stk.top().first < A[j]) stk.push(make_pair(A[j], 1));
				while (++ stk.top().second > mid) {
					tmp = mid == 1 ? 1 : stk.top().first;
					if (tmp == 1) goto break_label;
					stk.pop();
					if (stk.empty() || stk.top().first != tmp - 1) stk.push(make_pair(tmp - 1, 1));
				}
			}
		}
		check = true;
		break_label:;
		(check ? max : ans) = mid;
	}
	cout << max;
	return 0;
}
