#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  T f = 1;
  x = 0;
  char s = getchar();
  while (s < '0' || s > '9') {
    if (s == '-') f = -1;
    s = getchar();
  }
  while (s >= '0' && s <= '9') {
    x = x * 10 + s - '0';
    s = getchar();
  }
  x *= f;
}
template <typename T>
void print(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) print(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
T Max(T x, T y) {
  return x > y ? x : y;
}
const int maxn = 3e5 + 5;
int n, a[maxn], tree[maxn], pos[maxn], cnt, ans;
unsigned long long ran[maxn], h[maxn], t[maxn];
int work(int pos) {
  int maxx = -1, res = 0;
  for (int i = pos + 1; a[i] != 1; ++i) {
    maxx = Max(maxx, a[i]);
    if (i >= maxx && i - maxx + 1 <= pos && (h[i] ^ h[i - maxx]) == t[maxx])
      res++;
  }
  return res;
}
int main() {
  read(n);
  srand(2005 - 12 - 30);
  a[n + 1] = 1;
  for (int i = 1; i <= n; ++i) read(a[i]);
  for (int i = 1; i <= n; ++i) ran[i] = rand() * rand();
  for (int i = 1; i <= n; ++i) t[i] = t[i - 1] ^ ran[i];
  for (int i = 1; i <= n; ++i) h[i] = h[i - 1] ^ ran[a[i]];
  for (int i = 1; i <= n; ++i)
    if (a[i] == 1) ans += work(i) + 1;
  a[n + 1] = 1;
  reverse(a + 1, a + 1 + n);
  for (int i = 1; i <= n; ++i) h[i] = h[i - 1] ^ ran[a[i]];
  for (int i = 1; i <= n; ++i)
    if (a[i] == 1) ans += work(i);
  print(ans);
  return 0;
}

### Prompt

Please create a solution in CPP to the following problem:

You have an array a_1, a_2, ..., a_n. 

Let's call some subarray a_l, a_{l + 1}, ... , a_r of this array a subpermutation if it contains all integers from 1 to r-l+1 exactly once. For example, array a = [2, 2, 1, 3, 2, 3, 1] contains 6 subarrays which are subpermutations: [a_2 ... a_3], [a_2 ... a_4], [a_3 ... a_3], [a_3 ... a_5], [a_5 ... a_7], [a_7 ... a_7].

You are asked to calculate the number of subpermutations.

Input

The first line contains one integer n (1 ≤ n ≤ 3 ⋅ 10^5).

The second line contains n integers a_1, a_2, ... , a_n (1 ≤ a_i ≤ n). 

This array can contain the same integers.

Output

Print the number of subpermutations of the array a.

Examples

Input


8
2 4 1 3 4 2 1 2


Output


7


Input


5
1 1 2 1 2


Output


6

Note

There are 7 subpermutations in the first test case. Their segments of indices are [1, 4], [3, 3], [3, 6], [4, 7], [6, 7], [7, 7] and [7, 8].

In the second test case 6 subpermutations exist: [1, 1], [2, 2], [2, 3], [3, 4], [4, 4] and [4, 5].

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  T f = 1;
  x = 0;
  char s = getchar();
  while (s < '0' || s > '9') {
    if (s == '-') f = -1;
    s = getchar();
  }
  while (s >= '0' && s <= '9') {
    x = x * 10 + s - '0';
    s = getchar();
  }
  x *= f;
}
template <typename T>
void print(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) print(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
T Max(T x, T y) {
  return x > y ? x : y;
}
const int maxn = 3e5 + 5;
int n, a[maxn], tree[maxn], pos[maxn], cnt, ans;
unsigned long long ran[maxn], h[maxn], t[maxn];
int work(int pos) {
  int maxx = -1, res = 0;
  for (int i = pos + 1; a[i] != 1; ++i) {
    maxx = Max(maxx, a[i]);
    if (i >= maxx && i - maxx + 1 <= pos && (h[i] ^ h[i - maxx]) == t[maxx])
      res++;
  }
  return res;
}
int main() {
  read(n);
  srand(2005 - 12 - 30);
  a[n + 1] = 1;
  for (int i = 1; i <= n; ++i) read(a[i]);
  for (int i = 1; i <= n; ++i) ran[i] = rand() * rand();
  for (int i = 1; i <= n; ++i) t[i] = t[i - 1] ^ ran[i];
  for (int i = 1; i <= n; ++i) h[i] = h[i - 1] ^ ran[a[i]];
  for (int i = 1; i <= n; ++i)
    if (a[i] == 1) ans += work(i) + 1;
  a[n + 1] = 1;
  reverse(a + 1, a + 1 + n);
  for (int i = 1; i <= n; ++i) h[i] = h[i - 1] ^ ran[a[i]];
  for (int i = 1; i <= n; ++i)
    if (a[i] == 1) ans += work(i);
  print(ans);
  return 0;
}

```