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 main()
{
	int N;
	cin >> N;
	vector<int> A(N);
	for (int i = 0; i < N; i++) {
		cin >> A[i];
	}
	auto B = A;
	sort(B.begin(), B.end());
	B.erase(unique(B.begin(), B.end()), B.end());
	if (A == B) {
		cout << 1 << endl;
		return 0;
	}
	int lb = 1, ub = 2e5;
	while (ub - lb > 1) {
		int d = (lb + ub) >> 1;
		bool ng = false;
		map<int, int> mp;
		for (int i = 1; i < N; i++) {
			if (A[i] > A[i - 1]) continue;
			if (mp.empty()) {
				mp[A[i] - 1] += 1;
			}
			else {
				while (!mp.empty() && mp.rbegin()->first > A[i] - 1) {
					mp.erase(mp.rbegin()->first);
				}
				mp[A[i] - 1] += 1;
				int tmp = A[i] - 1;
				while (tmp >= 0 && mp[tmp] >= d) {
					mp[tmp] -= d;
					--tmp;
					mp[tmp] += 1;
				}
				if (tmp < 0) {
					ng = true;
					break;
				}
			}
		}
		(!ng ? ub : lb) = d;
	}
	cout << ub << endl;
	return 0;
}
