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<cstdio>
#include<algorithm>
#include<map>
using namespace std;
int n, w[201000];
map<int, int>Map;
bool Pos(int K) {
	int i;
	Map.clear();
	for (i = 2; i <= n; i++) {
		if (w[i] > w[i - 1]) {
			continue;
		}
		while (!Map.empty()) {
			auto it = Map.end();
			it--;
			if (it->first <= w[i])break;
			Map.erase(it);
		}
		Map[w[i]]++;
		int pv = w[i];
		while(Map[pv] == K) {
			if (pv == 1)return false;
			Map[pv] -= K;
			pv--;
			Map[pv]++;
		}
	}
	return true;
}
int main() {
	int i, chk = 0;
	scanf("%d", &n);
	for (i = 1; i <= n; i++) {
		scanf("%d", &w[i]);
		if (i>1 && w[i] <= w[i - 1])chk = 1;
	}
	if (!chk) {
		puts("1");
		return 0;
	}
	int b = 2, e = n, mid, r = 0;
	while (b <= e) {
		mid = (b + e) >> 1;
		if (Pos(mid)) {
			r = mid;
			e = mid - 1;
		}
		else b = mid + 1;
	}
	printf("%d\n", r);
}