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 <map>
#include <vector>
#include <iostream>
using namespace std;
int main() {
	int N;
	cin >> N;
	vector<int> A(N);
	for (int i = 0; i < N; ++i) {
		cin >> A[i];
	}
	bool increasing = true;
	for (int i = 1; i < N; ++i) {
		if (A[i - 1] >= A[i]) increasing = false;
	}
	if (increasing) {
		cout << 1 << endl;
	}
	else {
		int L = 1, R = N + 1;
		while (R - L > 1) {
			int M = (L + R) >> 1;
			map<int, int> d;
			for (int j = 0; j < N; ++j) {
				if (d.lower_bound(A[j]) != d.end() && d[A[j]] == 0) d[A[j]] = 1;
				while (!d.empty() && (--d.end())->first > A[j]) {
					d.erase(--d.end());
				}
				if (d[A[j]] < M) {
					++d[A[j]];
				}
				else {
					int ptr = A[j];
					while (true) {
						d[ptr] = 1;
						if (d[ptr - 1] < M) {
							if (d[ptr - 1] == 0) d[ptr - 1] = 1;
							++d[ptr - 1];
							break;
						}
						else --ptr;
					}
				}
			}
			if (d.begin()->first <= 0) {
				L = M;
			}
			else {
				R = M;
			}
		}
		cout << R << endl;
	}
	return 0;
}