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>

const int MN = 200005;

int N, A[MN];

int stkp[MN], stkv[MN], tp;
inline bool check(int M) {
	tp = 0;
	for (int i = 1; i <= N; ++i) {
		if (A[i] <= A[i - 1]) {
			while (stkp[tp] > A[i]) --tp;
			int pos = A[i];
			while (pos) {
				if (stkp[tp] != pos || stkv[tp] != M - 1) {
					if (stkp[tp] != pos)
						stkp[++tp] = pos,
						stkv[tp] = 0;
					++stkv[tp];
					break;
				} else --tp, --pos;
			}
			if (!pos) return 0;
		}
	}
	return 1;
}

int main() {
	int ok = 1;
	scanf("%d", &N);
	for (int i = 1; i <= N; ++i) {
		scanf("%d", &A[i]);
		if (A[i] <= A[i - 1]) ok = 0;
	}
	if (ok) return puts("1"), 0;
	int lb = 2, rb = N, mid = 0, ans = 0;
	while (lb <= rb) {
		mid = (lb + rb) >> 1;
		if (check(mid)) ans = mid, rb = mid - 1;
		else lb = mid + 1;
	}
	printf("%d\n", ans);
	return 0;
}