#include <bits/stdc++.h>
using namespace std;
const int MOD = (int)1e9 + 7;
const int MAXN = (int)3e5 + 3;
const int infint = (int)1e9 + 3;
const long long inf = (long long)2e18;
struct node {
  int minf, tedf, mimm, tmimm, mipm, tmipm, min, max, lazymax, lazymin;
  node() {
    minf = infint, tedf = 0;
    mimm = infint, tmimm = 0;
    mipm = infint, tmipm = 0;
    min = infint, max = -infint;
    lazymax = -1, lazymin = -1;
  }
} seg[4 * MAXN];
void updmax(int node, int st, int en, int x) {
  seg[node].max = x;
  seg[node].mipm = st + seg[node].max, seg[node].tmipm = 1;
  seg[node].minf = seg[node].mimm + seg[node].max,
  seg[node].tedf = seg[node].tmimm;
  seg[node].lazymax = x;
  return;
}
void updmin(int node, int st, int en, int x) {
  seg[node].min = x;
  seg[node].mimm = st - seg[node].min, seg[node].tmimm = 1;
  seg[node].minf = seg[node].mipm - seg[node].min,
  seg[node].tedf = seg[node].tmipm;
  seg[node].lazymin = x;
}
void shift(int node, int st, int en) {
  int mid = (st + en) >> 1;
  if (seg[node].lazymax != -1)
    updmax(node << 1, st, mid, seg[node].lazymax),
        updmax(node << 1 | 1, mid, en, seg[node].lazymax);
  if (seg[node].lazymin != -1)
    updmin(node << 1, st, mid, seg[node].lazymin),
        updmin(node << 1 | 1, mid, en, seg[node].lazymin);
  seg[node].lazymax = seg[node].lazymin = -1;
}
node merge(node a, node b) {
  node c;
  c.min = min(a.min, b.min);
  c.max = max(a.max, b.max);
  c.minf = a.minf, c.tedf = a.tedf;
  if (b.minf < c.minf)
    c.minf = b.minf, c.tedf = b.tedf;
  else if (b.minf == c.minf)
    c.tedf += b.tedf;
  c.mimm = a.mimm, c.tmimm = a.tmimm;
  if (b.mimm < c.mimm)
    c.mimm = b.mimm, c.tmimm = b.tmimm;
  else if (b.mimm == c.mimm)
    c.tmimm += b.tmimm;
  c.mipm = a.mipm, c.tmipm = a.tmipm;
  if (b.mipm < c.mipm)
    c.mipm = b.mipm, c.tmipm = b.tmipm;
  else if (b.mipm == c.mipm)
    c.tmipm += b.tmipm;
  c.lazymax = -1, c.lazymin = -1;
  return c;
}
void updatemax(int node, int st, int en, int l, int r, int x) {
  if (l >= en || st >= r) return;
  if (l <= st && en <= r) {
    updmax(node, st, en, x);
    return;
  }
  int mid = (st + en) >> 1;
  shift(node, st, en);
  updatemax(node << 1, st, mid, l, r, x);
  updatemax(node << 1 | 1, mid, en, l, r, x);
  seg[node] = merge(seg[node << 1], seg[node << 1 | 1]);
}
void updatemin(int node, int st, int en, int l, int r, int x) {
  if (l >= en || st >= r) return;
  if (l <= st && en <= r) {
    updmin(node, st, en, x);
    return;
  }
  int mid = (st + en) >> 1;
  shift(node, st, en);
  updatemin(node << 1, st, mid, l, r, x);
  updatemin(node << 1 | 1, mid, en, l, r, x);
  seg[node] = merge(seg[node << 1], seg[node << 1 | 1]);
}
node emp;
node get(int node, int st, int en, int l, int r) {
  if (l >= en || st >= r) {
    emp.minf = infint, emp.tedf = 0;
    emp.mimm = infint, emp.tmimm = 0;
    emp.mipm = infint, emp.tmipm = 0;
    emp.min = infint, emp.max = -infint;
    emp.lazymax = -1, emp.lazymin = -1;
    return emp;
  }
  if (l <= st && en <= r) return seg[node];
  int mid = (st + en) >> 1;
  shift(node, st, en);
  return merge(get(node << 1, st, mid, l, r),
               get(node << 1 | 1, mid, en, l, r));
}
int n, a[MAXN], s[MAXN], g[MAXN];
int zero[MAXN], oc[MAXN], prv[MAXN];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 0; i < 4 * MAXN; i++) seg[i] = node();
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i]--;
  }
  for (int i = 0; i < n; i++)
    if (a[i] == 0)
      zero[i] = i;
    else if (i == 0)
      zero[i] = -1;
    else
      zero[i] = zero[i - 1];
  memset(oc, -1, sizeof oc);
  for (int i = 0; i < n; i++) {
    prv[i] = oc[a[i]], oc[a[i]] = i;
    if (i) prv[i] = max(prv[i], prv[i - 1]);
  }
  for (int i = 0; i < n; i++) prv[i]++;
  stack<int> S;
  for (int i = 0; i < n; i++) {
    while (!S.empty() && a[S.top()] > a[i]) S.pop();
    if (S.size())
      s[i] = S.top();
    else
      s[i] = -1;
    S.push(i);
  }
  while (S.size()) S.pop();
  for (int i = 0; i < n; i++) {
    while (!S.empty() && a[S.top()] < a[i]) S.pop();
    if (S.size())
      g[i] = S.top();
    else
      g[i] = -1;
    S.push(i);
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    updatemin(1, 0, n, s[i] + 1, i + 1, a[i]);
    updatemax(1, 0, n, g[i] + 1, i + 1, a[i]);
    if (prv[i] <= zero[i]) {
      node cur = get(1, 0, n, prv[i], zero[i] + 1);
      if (cur.minf == i) ans += cur.tedf;
    }
  }
  cout << ans;
}

### Prompt

Your task is to create a Cpp solution 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;
const int MOD = (int)1e9 + 7;
const int MAXN = (int)3e5 + 3;
const int infint = (int)1e9 + 3;
const long long inf = (long long)2e18;
struct node {
  int minf, tedf, mimm, tmimm, mipm, tmipm, min, max, lazymax, lazymin;
  node() {
    minf = infint, tedf = 0;
    mimm = infint, tmimm = 0;
    mipm = infint, tmipm = 0;
    min = infint, max = -infint;
    lazymax = -1, lazymin = -1;
  }
} seg[4 * MAXN];
void updmax(int node, int st, int en, int x) {
  seg[node].max = x;
  seg[node].mipm = st + seg[node].max, seg[node].tmipm = 1;
  seg[node].minf = seg[node].mimm + seg[node].max,
  seg[node].tedf = seg[node].tmimm;
  seg[node].lazymax = x;
  return;
}
void updmin(int node, int st, int en, int x) {
  seg[node].min = x;
  seg[node].mimm = st - seg[node].min, seg[node].tmimm = 1;
  seg[node].minf = seg[node].mipm - seg[node].min,
  seg[node].tedf = seg[node].tmipm;
  seg[node].lazymin = x;
}
void shift(int node, int st, int en) {
  int mid = (st + en) >> 1;
  if (seg[node].lazymax != -1)
    updmax(node << 1, st, mid, seg[node].lazymax),
        updmax(node << 1 | 1, mid, en, seg[node].lazymax);
  if (seg[node].lazymin != -1)
    updmin(node << 1, st, mid, seg[node].lazymin),
        updmin(node << 1 | 1, mid, en, seg[node].lazymin);
  seg[node].lazymax = seg[node].lazymin = -1;
}
node merge(node a, node b) {
  node c;
  c.min = min(a.min, b.min);
  c.max = max(a.max, b.max);
  c.minf = a.minf, c.tedf = a.tedf;
  if (b.minf < c.minf)
    c.minf = b.minf, c.tedf = b.tedf;
  else if (b.minf == c.minf)
    c.tedf += b.tedf;
  c.mimm = a.mimm, c.tmimm = a.tmimm;
  if (b.mimm < c.mimm)
    c.mimm = b.mimm, c.tmimm = b.tmimm;
  else if (b.mimm == c.mimm)
    c.tmimm += b.tmimm;
  c.mipm = a.mipm, c.tmipm = a.tmipm;
  if (b.mipm < c.mipm)
    c.mipm = b.mipm, c.tmipm = b.tmipm;
  else if (b.mipm == c.mipm)
    c.tmipm += b.tmipm;
  c.lazymax = -1, c.lazymin = -1;
  return c;
}
void updatemax(int node, int st, int en, int l, int r, int x) {
  if (l >= en || st >= r) return;
  if (l <= st && en <= r) {
    updmax(node, st, en, x);
    return;
  }
  int mid = (st + en) >> 1;
  shift(node, st, en);
  updatemax(node << 1, st, mid, l, r, x);
  updatemax(node << 1 | 1, mid, en, l, r, x);
  seg[node] = merge(seg[node << 1], seg[node << 1 | 1]);
}
void updatemin(int node, int st, int en, int l, int r, int x) {
  if (l >= en || st >= r) return;
  if (l <= st && en <= r) {
    updmin(node, st, en, x);
    return;
  }
  int mid = (st + en) >> 1;
  shift(node, st, en);
  updatemin(node << 1, st, mid, l, r, x);
  updatemin(node << 1 | 1, mid, en, l, r, x);
  seg[node] = merge(seg[node << 1], seg[node << 1 | 1]);
}
node emp;
node get(int node, int st, int en, int l, int r) {
  if (l >= en || st >= r) {
    emp.minf = infint, emp.tedf = 0;
    emp.mimm = infint, emp.tmimm = 0;
    emp.mipm = infint, emp.tmipm = 0;
    emp.min = infint, emp.max = -infint;
    emp.lazymax = -1, emp.lazymin = -1;
    return emp;
  }
  if (l <= st && en <= r) return seg[node];
  int mid = (st + en) >> 1;
  shift(node, st, en);
  return merge(get(node << 1, st, mid, l, r),
               get(node << 1 | 1, mid, en, l, r));
}
int n, a[MAXN], s[MAXN], g[MAXN];
int zero[MAXN], oc[MAXN], prv[MAXN];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 0; i < 4 * MAXN; i++) seg[i] = node();
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i]--;
  }
  for (int i = 0; i < n; i++)
    if (a[i] == 0)
      zero[i] = i;
    else if (i == 0)
      zero[i] = -1;
    else
      zero[i] = zero[i - 1];
  memset(oc, -1, sizeof oc);
  for (int i = 0; i < n; i++) {
    prv[i] = oc[a[i]], oc[a[i]] = i;
    if (i) prv[i] = max(prv[i], prv[i - 1]);
  }
  for (int i = 0; i < n; i++) prv[i]++;
  stack<int> S;
  for (int i = 0; i < n; i++) {
    while (!S.empty() && a[S.top()] > a[i]) S.pop();
    if (S.size())
      s[i] = S.top();
    else
      s[i] = -1;
    S.push(i);
  }
  while (S.size()) S.pop();
  for (int i = 0; i < n; i++) {
    while (!S.empty() && a[S.top()] < a[i]) S.pop();
    if (S.size())
      g[i] = S.top();
    else
      g[i] = -1;
    S.push(i);
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    updatemin(1, 0, n, s[i] + 1, i + 1, a[i]);
    updatemax(1, 0, n, g[i] + 1, i + 1, a[i]);
    if (prv[i] <= zero[i]) {
      node cur = get(1, 0, n, prv[i], zero[i] + 1);
      if (cur.minf == i) ans += cur.tedf;
    }
  }
  cout << ans;
}

```