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 <stdio.h>
#include <map>
using namespace std;

int N,A[200200];

bool chk(int d)
{
	map<int, int> chk;
	for (int i=1;i<N;i++) if (A[i-1] >= A[i]){
		int x = A[i];
		while (1){
			auto I = chk.lower_bound(x+1);
			if (I != chk.end()) chk.erase(I);
			else break;
		}
		while (x > 0){
			auto I = chk.find(x);
			int v = (I == chk.end()) ? 0 : I->second;
			if (v + 1 == d){
				chk.erase(x); x--;
			}
			else{
				if (I == chk.end()) chk[x] = 1;
				else I->second++;
				break;
			}
		}
		if (x == 0) return false;
	}
	return true;
}

int main()
{
	scanf ("%d",&N);
	for (int i=0;i<N;i++) scanf ("%d",&A[i]);

	bool g = 1;
	for (int i=1;i<N;i++) if (A[i-1] >= A[i]) g = 0;
	if (g){
		puts("1");
		return 0;
	}

	int l = 1, r = N;
	while (l + 1 < r){
		int m = (l + r) / 2;
		if (chk(m)) r = m;
		else l = m;
	}
	printf ("%d\n",r);

	return 0;
}