#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
const int maxN = 1e6 + 1;
const int mod = 1e9 + 7;
const ll oo = 1e9;
int n, a[maxN];
pair<int, int> d[maxN];
int f[maxN], e[maxN];
inline void FastInput() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
}
void ReadInput() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    e[i] = oo;
    d[i] = {a[i], i - a[i]};
  }
  sort(d + 1, d + n + 1, [](pair<int, int> p, pair<int, int> q) {
    return (p.first < q.first || (p.first == q.first && p.second > q.second));
  });
}
void Solve() {
  for (int i = 1; i <= n; i++) {
    if (d[i].second < 0) continue;
    f[i] = upper_bound(e + 1, e + n + 1, d[i].second) - e;
    e[f[i]] = d[i].second;
  }
  cout << *max_element(f + 1, f + n + 1);
}
int main() {
  FastInput();
  ReadInput();
  Solve();
}

### Prompt

In Cpp, your task is to solve 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;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
const int maxN = 1e6 + 1;
const int mod = 1e9 + 7;
const ll oo = 1e9;
int n, a[maxN];
pair<int, int> d[maxN];
int f[maxN], e[maxN];
inline void FastInput() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
}
void ReadInput() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    e[i] = oo;
    d[i] = {a[i], i - a[i]};
  }
  sort(d + 1, d + n + 1, [](pair<int, int> p, pair<int, int> q) {
    return (p.first < q.first || (p.first == q.first && p.second > q.second));
  });
}
void Solve() {
  for (int i = 1; i <= n; i++) {
    if (d[i].second < 0) continue;
    f[i] = upper_bound(e + 1, e + n + 1, d[i].second) - e;
    e[f[i]] = d[i].second;
  }
  cout << *max_element(f + 1, f + n + 1);
}
int main() {
  FastInput();
  ReadInput();
  Solve();
}

```