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 rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pair
 
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int INF = 1e9 + 7;
 
int n, a[200005];
 
bool check(int m)
{
	if(m == 1) {
		for(int i = 1; i < n; i ++)
		if(a[i] <= a[i - 1]) return false;
		return true;
	}
	map<int, int> cur;
	for(int i = 1; i < n; i ++) {
		if(a[i] > a[i - 1]) continue;
		map<int, int>::iterator cc;
		while((cc = cur.upper_bound(a[i])) != cur.end()) cur.erase(cc);
		cur[a[i]] ++;
		int cp = a[i];
		while(cur[cp] >= m) {
			cur.erase(cp);
			cp --;
			cur[cp] ++;
			if(cp == 0) return false;
		}
	}
	return true;
}
 
int main()
{
	scanf("%d", &n);
	rep(i, n) scanf("%d", &a[i]);
	int l = 1, r = n;
	while(l < r) {
		int mid = (l + r) >> 1;
		if(check(mid)) r = mid;
		else l = mid + 1;
	}
	printf("%d\n", r);
	return 0;
}