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 <bits/stdc++.h>
#define REP(i, a, n) for (ll i = ((ll) a); i < ((ll) n); i++)
using namespace std;
typedef long long ll;

ll N, A[200000];

bool check() {
  REP(i, 0, N - 1) if (A[i] >= A[i + 1]) return false;
  return true;
}

bool ok(ll x) {
  map<ll, ll> mp;
  ll k = A[0];

  REP(i, 1, N) {
    if (A[i] <= k) {
      mp.erase(mp.lower_bound(A[i]), mp.end());
      for (ll j = A[i] - 1;; j--) {
        mp[j]++;
        if (mp[j] < x) break;
        mp[j] = 0;
        if (j == 0) return false;
      }
    }
    k = A[i];
  }

  return true;
}

int main(void) {
  cin >> N;
  REP(i, 0, N) cin >> A[i];

  if (check()) {
    cout << 1 << endl;
    return 0;
  }

  ll l = 1, h = N;
  while (h - l > 1) {
    ll m = (l + h) / 2;
    if (ok(m)) h = m;
    else l = m;
  }
  cout << h << endl;
}