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 <cstring>
#include <algorithm>

int n;
int w[233333];

int q[233333][2], t;
bool check(int a, int i = 1, int ls = 0){
	q[t = 1][0] = 0, q[t][1] = 0;
	q[++t][0] = 1, q[t][1] = 1;
	(w[1] == 1) && (i++);
	for(i; i <= n; i++){
		if(q[1][1]) return false;
		ls = w[i];
		if(q[t][0] < ls) q[++t][0] = ls, q[t][1] = 1;
		else{
			while(t){
				if(q[t][0] == ls){
					if(q[t][1] < a) {q[t][1]++; break;}
					else t--, ls--;
				}
				else if(q[t][0] < ls){
					q[++t][0] = ls, q[t][1] = 2;
					if(a == 1) return false;
					break;
				}
				else t--;
			}
			if(q[t][0] != w[i]) q[++t][0] = w[i], q[t][1] = 1;
		}
	}
	if(q[1][1]) return false;
	return true;
}

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