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
N = int(input())
A = list(map(int,input().split()))
if A == sorted(A) and len(A) == len(set(A)):
  print(1)
  exit(0)

def check(X):
  idx = [0]
  ltr = [0]
  for a in A:
    if idx[-1] < a:
      idx.append(a)
      ltr.append(0)
    else:
      while True:
        while idx[-1] > a:
          idx.pop()
          ltr.pop()
        if idx[-1] != a:
          idx.append(a)
          ltr.append(0)
        if idx[-1] == 0:
          return False
        ltr[-1] += 1
        if ltr[-1] < X:
          break
        a = idx[-1] - 1
        idx.pop()
        ltr.pop()
  return ltr[0] == 0

t = [1, N]
while t[1] - t[0] > 1:
  mid = (t[0] + t[1]) // 2
  t[check(mid)] = mid
print(t[1])
