#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
template <typename T, size_t N>
int SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
int SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, int x1 = 0, int x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, int x1 = 0, int x2 = 1e9) {
  string t = "";
  for (int __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), int x1 = 0, int x2 = 1e9, C... coords);
int l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), int x1, int x2, C... coords) {
  int rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void dbgm() { ; }
template <typename Heads, typename... Tails>
void dbgm(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  dbgm(T...);
}
const long long MOD = (int)1e9 + 7;
string ascii_lowercase = "abcdefghijklmnopqrstuvwxyz";
string ascii_uppercase = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
struct hashLL {
  size_t operator()(long long x) const {
    x = (x ^ (x >> 30)) * UINT64_C(0xbf58476d1ce4e5b9);
    x = (x ^ (x >> 27)) * UINT64_C(0x94d049bb133111eb);
    x = x ^ (x >> 31);
    return x;
  }
};
long long inv(long long a, long long b) {
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}
const long long INF = 1e6;
unordered_map<int, int, custom_hash> mp;
long long gcd(long long a, long long b, long long &x, long long &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long x1, y1;
  long long d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
long long distsq(long long x1, long long y1, long long x2, long long y2) {
  return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
}
long long n, m;
const int N = 200005;
pair<long long, unordered_map<long long, long long>> segtree[2 * N];
void upd(long long p, long long val) {
  p += N;
  segtree[p].first = 1;
  segtree[p].second[val] = 1;
  for (; p >= 1; p >>= 1) {
    segtree[p >> 1].first = segtree[p].first + segtree[p ^ 1].first;
    long long x = 0, y = 0;
    if (segtree[p].second.count(val)) x = segtree[p].second[val];
    if (segtree[p ^ 1].second.count(val)) y = segtree[p ^ 1].second[val];
    segtree[p >> 1].second[val] = x + y;
  }
}
long long query(int l, int r) {
  long long ans = 0;
  l += N;
  r += N;
  while (l < r) {
    if (l & 1) {
      ans += segtree[l++].first;
    }
    if (r & 1) ans += segtree[--r].first;
    l /= 2;
    r /= 2;
  }
  return ans;
}
void dell(long long val) {
  vector<int> stk;
  stk.push_back(1);
  while (!stk.empty()) {
    int idx = stk.back();
    stk.pop_back();
    if (idx >= 2 * N - 1) continue;
    if (segtree[idx].second.count(val) == 0) continue;
    segtree[idx].first -= segtree[idx].second[val];
    segtree[idx].second.erase(val);
    stk.push_back(idx * 2);
    stk.push_back(idx * 2 + 1);
  }
}
int main() {
  cin >> n;
  long long ai;
  long long ans = 0;
  for (long long i = 1; i <= n; i++) {
    cin >> ai;
    ans += query(1, min(ai + 1, i));
    if (ai > i) upd(i, ai);
    dell(i);
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Generate a cpp solution to the following problem:

One day Polycarp decided to rewatch his absolute favourite episode of well-known TV series "Tufurama". He was pretty surprised when he got results only for season 7 episode 3 with his search query of "Watch Tufurama season 3 episode 7 online full hd free". This got Polycarp confused — what if he decides to rewatch the entire series someday and won't be able to find the right episodes to watch? Polycarp now wants to count the number of times he will be forced to search for an episode using some different method.

TV series have n seasons (numbered 1 through n), the i-th season has ai episodes (numbered 1 through ai). Polycarp thinks that if for some pair of integers x and y (x < y) exist both season x episode y and season y episode x then one of these search queries will include the wrong results. Help Polycarp to calculate the number of such pairs!

Input

The first line contains one integer n (1 ≤ n ≤ 2·105) — the number of seasons.

The second line contains n integers separated by space a1, a2, ..., an (1 ≤ ai ≤ 109) — number of episodes in each season.

Output

Print one integer — the number of pairs x and y (x < y) such that there exist both season x episode y and season y episode x.

Examples

Input

5
1 2 3 4 5


Output

0


Input

3
8 12 7


Output

3


Input

3
3 2 1


Output

2

Note

Possible pairs in the second example:

  1. x = 1, y = 2 (season 1 episode 2 <image> season 2 episode 1); 
  2. x = 2, y = 3 (season 2 episode 3 <image> season 3 episode 2); 
  3. x = 1, y = 3 (season 1 episode 3 <image> season 3 episode 1). 



In the third example:

  1. x = 1, y = 2 (season 1 episode 2 <image> season 2 episode 1); 
  2. x = 1, y = 3 (season 1 episode 3 <image> season 3 episode 1). 

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
template <typename T, size_t N>
int SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
int SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, int x1 = 0, int x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, int x1 = 0, int x2 = 1e9) {
  string t = "";
  for (int __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), int x1 = 0, int x2 = 1e9, C... coords);
int l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), int x1, int x2, C... coords) {
  int rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void dbgm() { ; }
template <typename Heads, typename... Tails>
void dbgm(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  dbgm(T...);
}
const long long MOD = (int)1e9 + 7;
string ascii_lowercase = "abcdefghijklmnopqrstuvwxyz";
string ascii_uppercase = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
struct hashLL {
  size_t operator()(long long x) const {
    x = (x ^ (x >> 30)) * UINT64_C(0xbf58476d1ce4e5b9);
    x = (x ^ (x >> 27)) * UINT64_C(0x94d049bb133111eb);
    x = x ^ (x >> 31);
    return x;
  }
};
long long inv(long long a, long long b) {
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}
const long long INF = 1e6;
unordered_map<int, int, custom_hash> mp;
long long gcd(long long a, long long b, long long &x, long long &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long x1, y1;
  long long d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
long long distsq(long long x1, long long y1, long long x2, long long y2) {
  return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
}
long long n, m;
const int N = 200005;
pair<long long, unordered_map<long long, long long>> segtree[2 * N];
void upd(long long p, long long val) {
  p += N;
  segtree[p].first = 1;
  segtree[p].second[val] = 1;
  for (; p >= 1; p >>= 1) {
    segtree[p >> 1].first = segtree[p].first + segtree[p ^ 1].first;
    long long x = 0, y = 0;
    if (segtree[p].second.count(val)) x = segtree[p].second[val];
    if (segtree[p ^ 1].second.count(val)) y = segtree[p ^ 1].second[val];
    segtree[p >> 1].second[val] = x + y;
  }
}
long long query(int l, int r) {
  long long ans = 0;
  l += N;
  r += N;
  while (l < r) {
    if (l & 1) {
      ans += segtree[l++].first;
    }
    if (r & 1) ans += segtree[--r].first;
    l /= 2;
    r /= 2;
  }
  return ans;
}
void dell(long long val) {
  vector<int> stk;
  stk.push_back(1);
  while (!stk.empty()) {
    int idx = stk.back();
    stk.pop_back();
    if (idx >= 2 * N - 1) continue;
    if (segtree[idx].second.count(val) == 0) continue;
    segtree[idx].first -= segtree[idx].second[val];
    segtree[idx].second.erase(val);
    stk.push_back(idx * 2);
    stk.push_back(idx * 2 + 1);
  }
}
int main() {
  cin >> n;
  long long ai;
  long long ans = 0;
  for (long long i = 1; i <= n; i++) {
    cin >> ai;
    ans += query(1, min(ai + 1, i));
    if (ai > i) upd(i, ai);
    dell(i);
  }
  cout << ans << endl;
  return 0;
}

```