#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 10;
struct BIT {
  int n;
  vector<int> bit;
  BIT(int _n) {
    n = _n;
    bit = vector<int>(n, -n);
  }
  int mx(int k) {
    int s = -n;
    k++;
    while (k >= 1) {
      s = max(s, bit[k]);
      k -= k & -k;
    }
    return s;
  }
  void update(int p, int value) {
    p++;
    while (p <= n) {
      bit[p] = max(bit[p], value);
      p += p & -p;
    }
  }
};
vector<int> v[MAXN];
int main() {
  int n;
  cin >> n;
  BIT bit(MAXN);
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    v[x].push_back(i);
  }
  bit.update(0, 0);
  int ans = 0;
  for (int i = 1; i < MAXN; i++) {
    reverse(v[i].begin(), v[i].end());
    for (auto x : v[i]) {
      if (x < i) continue;
      int res = bit.mx(x - i) + 1;
      ans = max(ans, res);
      bit.update(x - i, res);
    }
  }
  cout << ans << "\n";
  return 0;
}

### Prompt

Generate a CPP solution to the following problem:

Mr. Chanek gives you a sequence a indexed from 1 to n. Define f(a) as the number of indices where a_i = i. 

You can pick an element from the current sequence and remove it, then concatenate the remaining elements together. For example, if you remove the 3-rd element from the sequence [4, 2, 3, 1], the resulting sequence will be [4, 2, 1]. 

You want to remove some elements from a in order to maximize f(a), using zero or more operations. Find the largest possible f(a).

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the initial length of the sequence.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 2 ⋅ 10^5) — the initial sequence a.

Output

Output an integer denoting the largest f(a) that can be obtained by doing zero or more operations.

Examples

Input


7
2 1 4 2 5 3 7


Output


3


Input


4
4 2 3 1


Output


2

Note

In the first example, f(A) = 3 by doing the following operations.

[2,1,4,2,5,3,7] → [2,1,2,5,3,7] → [1,2,5,3,7] → [1,2,5,3] → [1,2,3]

In the second example, f(A) = 2 and no additional operation is needed.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 10;
struct BIT {
  int n;
  vector<int> bit;
  BIT(int _n) {
    n = _n;
    bit = vector<int>(n, -n);
  }
  int mx(int k) {
    int s = -n;
    k++;
    while (k >= 1) {
      s = max(s, bit[k]);
      k -= k & -k;
    }
    return s;
  }
  void update(int p, int value) {
    p++;
    while (p <= n) {
      bit[p] = max(bit[p], value);
      p += p & -p;
    }
  }
};
vector<int> v[MAXN];
int main() {
  int n;
  cin >> n;
  BIT bit(MAXN);
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    v[x].push_back(i);
  }
  bit.update(0, 0);
  int ans = 0;
  for (int i = 1; i < MAXN; i++) {
    reverse(v[i].begin(), v[i].end());
    for (auto x : v[i]) {
      if (x < i) continue;
      int res = bit.mx(x - i) + 1;
      ans = max(ans, res);
      bit.update(x - i, res);
    }
  }
  cout << ans << "\n";
  return 0;
}

```