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 = [int(i) - 1 for i in input().split()]

def check(m) :
  dp = [0] * 40
  for i in range(1, N) :
    if A[i] <= A[i-1] and A[i] < 40 :
      for j in range(A[i] + 1, 40) :
        dp[j] = 0
      dp[A[i]] += 1
      for j in range(A[i], 0, -1) :
        if dp[j] >= m :
          dp[j-1] += 1
          dp[j] %= m
      if dp[0] >= m :
        return False
        
  return True

ng, ok = 0, N
for i in range(1, N) :
  if A[i] <= A[i-1] :
    ng = 1
    
while ok - ng > 1 :
  m = (ok + ng) // 2
  
  if check(m) :
    ok = m
  else :
    ng = m
    
print(ok)