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;
typedef long long ll;
const ll MOD = 998244353;
const double EPS = 1e-10;
typedef pair<int, int> P;
int A[200000];
int main() {
	int N;
	cin >> N;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
	}
	bool one = 1;
	for (int i = 1; i < N; i++) {
		if (A[i] <= A[i - 1]) {
			one = 0;
			break;
		}
	}
	if (one) {
		cout << 1 << endl;
		return 0;
	}
	int l = 1, r = 1 << 30;
	while ((r - l) > 1) {
		int m = (l + r) / 2;
		map<int, int> mp;
		bool ok = 1;
		for (int i = 1; i < N; i++) {
			if (A[i - 1] < A[i]) continue;
			auto itr = mp.lower_bound(A[i]);
			mp.erase(itr, mp.end());
			int j = A[i] - 1;
			while (j >= 0) {
				if (mp.find(j) != mp.end() && mp[j] == m - 1) {
					j--;
					continue;
				}
				mp[j]++;
				itr = mp.upper_bound(j);
				mp.erase(itr, mp.end());
				break;
			}
			if (j < 0 || mp[j] >= m) {
				ok = 0;
				break;
			}
		}
		if (ok) r = m;
		else l = m;
	}
	cout << r << endl;
}