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 A[200055];

int N;

bool isp(int X) {
	map<int, int> PQ;
	for(int i = 2; i <= N; i++) {
		if(A[i-1] < A[i]) continue;
		for(; !PQ.empty();) {
			auto it = prev(PQ.end());
			if(it->first < A[i]) break;
			PQ.erase(it);
		}
		for(int x = A[i]-1;; x--) {
			if(x < 0) return false;
			int k = 0;
			auto it = PQ.find(x);
			if(PQ.end() != it) {
				k = it->second;
				PQ.erase(it);
			}
			k++;
			if(k < X) {
				PQ.insert({x, k});
				break;
			}
		}
	}
	return true;
}

int getAns() {
	int s = 2, e = N; for(int m; s < e;) {
		m = (s+e) >> 1;
		if(isp(m)) e = m;
		else s = m+1;
	}
	return s;
}

int main() {
	ios::sync_with_stdio(false);

	cin >> N;
	for(int i = 1; i <= N; i++) cin >> A[i];

	{
		bool flag = true;
		for(int i = 1; i < N; i++)
			flag &= A[i] < A[i+1];
		if(flag) {
			puts("1");
			return 0;
		}
	}

	cout << getAns() << endl;
	return 0;
}