#include <bits/stdc++.h>
using namespace std;
const int Max_N = 2e5, Inf = 1e9;
int n, P[Max_N * 2 + 5];
struct kk {
  int val, pos;
} a[Max_N + 5];
bool mycmp(kk x, kk y) {
  return x.val == y.val ? x.pos > y.pos : x.val < y.val;
}
int Ask(int x) {
  int ans = -Inf;
  for (x += n; x <= 2 * n; x += x & -x) ans = max(ans, P[x]);
  return ans;
}
void Add(int x, int val) {
  for (x += n; x; x -= x & -x) P[x] = max(P[x], val);
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].val), a[i].pos = i;
  sort(a + 1, a + n + 1, mycmp);
  for (int i = 0; i <= 2 * n; i++) P[i] = -Inf;
  Add(0, 0);
  for (int i = 1; i <= n; i++) {
    int now = Ask(a[i].val - a[i].pos) + 1;
    Add(a[i].val - a[i].pos, now);
  }
  printf("%d\n", Ask(-n + 1));
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 Max_N = 2e5, Inf = 1e9;
int n, P[Max_N * 2 + 5];
struct kk {
  int val, pos;
} a[Max_N + 5];
bool mycmp(kk x, kk y) {
  return x.val == y.val ? x.pos > y.pos : x.val < y.val;
}
int Ask(int x) {
  int ans = -Inf;
  for (x += n; x <= 2 * n; x += x & -x) ans = max(ans, P[x]);
  return ans;
}
void Add(int x, int val) {
  for (x += n; x; x -= x & -x) P[x] = max(P[x], val);
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i].val), a[i].pos = i;
  sort(a + 1, a + n + 1, mycmp);
  for (int i = 0; i <= 2 * n; i++) P[i] = -Inf;
  Add(0, 0);
  for (int i = 1; i <= n; i++) {
    int now = Ask(a[i].val - a[i].pos) + 1;
    Add(a[i].val - a[i].pos, now);
  }
  printf("%d\n", Ask(-n + 1));
  return 0;
}

```