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>

#define N 200010 

using namespace std;

typedef long long ll;


int a[N], n;

map <ll, ll> MP;

bool check(int x) {
	MP.clear();
	for (int i = 2; i <= n; i ++ ) {
		if (a[i - 1] >= a[i]) {
			if (x == 1) {
				return false;
			}
			while (!MP.empty()) {
				ll mx = MP.rbegin() -> first;
				if (mx > a[i]) {
					MP.erase(mx);
				}
				else {
					break;
				}
			}

			int j = a[i];
			while (j > 0 && MP[j] + 1 == x) {
				MP.erase(j);
				j -- ;
			}
			if (!j) {
				return false;
			}
			MP[j] ++ ;
		}
	}
	return true;
}


int main() {
	scanf("%d",&n);
	for (int i = 1; i <= n; i ++ ) {
		scanf("%d",&a[i]);
	}

	int l = 1, r = n, ans = n;
	while (l <= r) {
		int mid = (l + r) >> 1;
		if (check(mid)) {
			ans = mid;
			r = mid - 1;
		}
		else {
			l = mid + 1;
		}
	}
	cout << ans << endl ;
	return 0;
}