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;

const int N = 200010;

typedef pair<int, int> P;

int A[N], n;

inline bool check(int mid) {
	set<P> s;
	for (int i = 2; i <= n; i++) if (A[i] <= A[i - 1]) {
		while (s.size() && s.rbegin() -> first > A[i]) s.erase(*s.rbegin());
		for (int j = A[i]; ; j--) {
			if (!j) return false;
			if (s.size() && j == s.rbegin() -> first) {
				if (s.rbegin() -> second < mid - 1) {
					auto t = *s.rbegin(); s.erase(t), t.second++;
					s.insert(t); break;	
				} else s.erase(*s.rbegin());
			} else {
				if (mid == 1) return false;
				s.insert(P(j, 1)); break;
			}
		} 
	}
	return true;
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) scanf("%d", &A[i]);
	int l = 1, r = n, mid, ans = -1;
	while (l <= r) {
		mid = (l + r) >> 1;
		if (check(mid)) r = mid - 1, ans = mid;
		else l = mid + 1;
	}
	printf("%d\n", ans);
}//