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;

static long long N, A[200000];
map<long long, long long> mp;

bool check(long long X) {
	mp.clear();
	for (int i = 1; i < N; i++) {
		if (A[i - 1] >= A[i]) {
			auto it = mp.upper_bound(A[i]);
			mp.erase(it, mp.end());
			mp[A[i]]++;
			long long NOW = A[i];
			while (mp[NOW] == X) {
				mp.erase(NOW);
				NOW--;
				if (NOW == 0) return false;
				mp[NOW]++;
			}
		}
	}
	return true;
}

int main() {
	cin >> N;
	for (int i = 0; i < N; i++) cin >> A[i];
	bool check1 = true;
	for (int i = 0; i < N - 1; i++) {
		if (A[i + 1] <= A[i]) check1 = false;
	}
	if (check1) {
		cout << 1 << endl;
		return 0;
	}
	long long L = 1, R = N + 1;
	while (R - L > 1) {
		long long MID = (L + R) / 2;
		check(MID) ? R = MID : L = MID;
	}
	cout << R << endl;
}