#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;
template <typename...>
static inline int getchar_unlocked(void) {
  return getchar();
}
template <typename...>
static inline void putchar_unlocked(int c) {
  putchar(c);
}
void reader(int& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
void reader(ll& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
int reader(char c[]) {
  int i, s = 0;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c[s++] = i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c[s++] = i;
  }
  c[s] = '\0';
  return s;
}
int reader(string& c) {
  int i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c.push_back(i);
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c.push_back(i);
  };
  return ((int)c.size());
}
template <class T, class S>
void reader(T& x, S& y) {
  reader(x);
  reader(y);
}
template <class T, class S, class U>
void reader(T& x, S& y, U& z) {
  reader(x);
  reader(y);
  reader(z);
}
template <class T, class S, class U, class V>
void reader(T& x, S& y, U& z, V& w) {
  reader(x);
  reader(y);
  reader(z);
  reader(w);
}
void writer(int x, char c) {
  int s = 0, m = 0;
  char f[10];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(ll x, char c) {
  int s = 0, m = 0;
  char f[20];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(const char c[]) {
  int i;
  for (i = 0; c[i] != '\0'; i++) putchar_unlocked(c[i]);
}
void writer(const string& x, char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
void writer(const char x[], char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
template <class T>
void writerLn(T x) {
  writer(x, '\n');
}
template <class T, class S>
void writerLn(T x, S y) {
  writer(x, ' ');
  writer(y, '\n');
}
template <class T, class S, class U>
void writerLn(T x, S y, U z) {
  writer(x, ' ');
  writer(y, ' ');
  writer(z, '\n');
}
template <class T>
void writerArr(T x[], int n) {
  if (!n) {
    putchar_unlocked('\n');
    return;
  }
  for (int i = 0; i < (n - 1); i++) writer(x[i], ' ');
  writer(x[n - 1], '\n');
}
template <class T>
void writerArr(vector<T>& x) {
  writerArr(x.data(), (int)x.size());
}
template <class T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
ll mod_pow(ll a, ll n, ll mod) {
  ll ret = 1;
  ll p = a % mod;
  while (n) {
    if (n & 1) ret = ret * p % mod;
    p = p * p % mod;
    n >>= 1;
  }
  return ret;
}
template <class T>
T extgcd(T a, T b, T& x, T& y) {
  for (T u = y = 1, v = x = 0; a;) {
    T q = b / a;
    swap(x -= q * u, u);
    swap(y -= q * v, v);
    swap(b -= q * a, a);
  }
  return b;
}
template <class T>
T mod_inv(T a, T m) {
  T x, y;
  extgcd(a, m, x, y);
  return (m + x % m) % m;
}
const int N = ((int)1e7) + 1;
bool prime[N];
vector<int> prs;
void init_prime() {
  memset(prime, 1, sizeof(prime));
  prime[0] = prime[1] = false;
  for (int i = 2; i < sizeof(prime); i++)
    if (prime[i])
      for (int j = i * 2; j < sizeof(prime); j += i) prime[j] = false;
  for (int i = 2; i < sizeof(prime); i++)
    if (prime[i]) prs.push_back(i);
}
int factors[N];
void init_factor() {
  for (int i = 2; i < N; i += 2) factors[i] = 2;
  for (int i = 3; i < N; i += 2) factors[i] = i;
  for (int i = 3; i < N; i += 2)
    if (factors[i] == i)
      for (int j = 3 * i; j < N; j += 2 * i) chmin(factors[j], i);
}
ll cnt1(int n) {
  ll ret = 0;
  static char di[((int)1e7) + 1];
  memset(di, 0, sizeof(char) * (n + 1));
  for (int i = 2; i <= n; i++) {
    int use = 1 - di[i];
    if (use == 0) continue;
    ll val = (n / i) * ll(n / i);
    ret += val * use;
    for (int j = i * 2; j <= n; j += i) {
      di[j] += use;
    }
  }
  int diagonal = n - 1;
  ret = (ret - diagonal) / 2;
  return ret;
}
ll solve(int n) {
  ll a = cnt1(n);
  ll b = 0;
  {
    static ll sm[((int)1e7) + 10];
    memset(sm, 0, sizeof(ll) * (n + 2));
    for (int i = 2; i <= n; i++) {
      sm[factors[i]]++;
    }
    sm[1] = 1;
    for (int i = 0; i < (n + 1); i++) sm[i + 1] += sm[i];
    for (int l = 0; l < (n); l++) {
      if (l <= 1) continue;
      const int rp = n / l;
      if (l >= rp) break;
      ll ccnt = sm[l] - sm[l - 1];
      ll rcnt = sm[rp] - sm[l];
      b += ccnt * rcnt;
    }
    for (int l = 0; l < (n); l++) {
      if (l <= 1) continue;
      ll ccnt = sm[l] - sm[l - 1];
      ll addd = ccnt * (ccnt - 1) / 2;
      b += addd;
    }
    b -= a;
  }
  ll dall = 0;
  {
    ll pcnt = 0;
    for (int i = n / 2 + 1; i <= n; i++)
      if (prime[i]) pcnt++;
    pcnt++;
    dall = (n - pcnt) * (n - pcnt - 1) / 2;
  }
  ll c = dall - a - b;
  return a + b * 2 + c * 3;
}
ll solve2(int n) {
  n++;
  static int di[1000][1000];
  memset(di, 0x1f, sizeof(di));
  for (int i = 0; i < (n); i++)
    for (int j = 0; j < (n); j++) {
      if (i == 0 || j == 0) continue;
      if (gcd(i, j) != 1) {
        di[i][j] = 1;
      }
    }
  for (int i = 0; i < (n); i++) di[i][i] = 0;
  for (int k = 0; k < (n); k++)
    for (int i = 0; i < (n); i++)
      for (int j = 0; j < (n); j++) chmin(di[i][j], di[i][k] + di[k][j]);
  ll ret = 0;
  int ec[4] = {};
  for (int i = 0; i < (n); i++)
    for (int j = i + 1; j < n; j++) {
      if (di[i][j] <= 10) {
        ret += di[i][j];
        if (di[i][j] >= 4) {
          cout << "?";
        }
        ec[di[i][j]]++;
        if (di[i][j] == 3) {
          printf("(%d, %d)\n", i, j);
        }
      }
    }
  writerArr(ec, 4);
  return ret;
}
void tst() {
  for (int i = 21; i <= 100; i++) {
    ll cur = solve(i);
    ll c2 = solve2(i);
    if (cur != c2) {
      cout << "?";
    }
    cout << cur << endl;
  }
}
int main() {
  init_prime();
  init_factor();
  int n;
  reader(n);
  cout << solve(n) << endl;
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

You are given a positive integer n. Let's build a graph on vertices 1, 2, ..., n in such a way that there is an edge between vertices u and v if and only if <image>. Let d(u, v) be the shortest distance between u and v, or 0 if there is no path between them. Compute the sum of values d(u, v) over all 1 ≤ u < v ≤ n.

The gcd (greatest common divisor) of two positive integers is the maximum positive integer that divides both of the integers.

Input

Single integer n (1 ≤ n ≤ 107).

Output

Print the sum of d(u, v) over all 1 ≤ u < v ≤ n.

Examples

Input

6


Output

8


Input

10


Output

44

Note

All shortest paths in the first example: 

  * <image>
  * <image>
  * <image>
  * <image>
  * <image>
  * <image>



There are no paths between other pairs of vertices.

The total distance is 2 + 1 + 1 + 2 + 1 + 1 = 8.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;
template <typename...>
static inline int getchar_unlocked(void) {
  return getchar();
}
template <typename...>
static inline void putchar_unlocked(int c) {
  putchar(c);
}
void reader(int& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
void reader(ll& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
int reader(char c[]) {
  int i, s = 0;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c[s++] = i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c[s++] = i;
  }
  c[s] = '\0';
  return s;
}
int reader(string& c) {
  int i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c.push_back(i);
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c.push_back(i);
  };
  return ((int)c.size());
}
template <class T, class S>
void reader(T& x, S& y) {
  reader(x);
  reader(y);
}
template <class T, class S, class U>
void reader(T& x, S& y, U& z) {
  reader(x);
  reader(y);
  reader(z);
}
template <class T, class S, class U, class V>
void reader(T& x, S& y, U& z, V& w) {
  reader(x);
  reader(y);
  reader(z);
  reader(w);
}
void writer(int x, char c) {
  int s = 0, m = 0;
  char f[10];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(ll x, char c) {
  int s = 0, m = 0;
  char f[20];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(const char c[]) {
  int i;
  for (i = 0; c[i] != '\0'; i++) putchar_unlocked(c[i]);
}
void writer(const string& x, char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
void writer(const char x[], char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
template <class T>
void writerLn(T x) {
  writer(x, '\n');
}
template <class T, class S>
void writerLn(T x, S y) {
  writer(x, ' ');
  writer(y, '\n');
}
template <class T, class S, class U>
void writerLn(T x, S y, U z) {
  writer(x, ' ');
  writer(y, ' ');
  writer(z, '\n');
}
template <class T>
void writerArr(T x[], int n) {
  if (!n) {
    putchar_unlocked('\n');
    return;
  }
  for (int i = 0; i < (n - 1); i++) writer(x[i], ' ');
  writer(x[n - 1], '\n');
}
template <class T>
void writerArr(vector<T>& x) {
  writerArr(x.data(), (int)x.size());
}
template <class T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
ll mod_pow(ll a, ll n, ll mod) {
  ll ret = 1;
  ll p = a % mod;
  while (n) {
    if (n & 1) ret = ret * p % mod;
    p = p * p % mod;
    n >>= 1;
  }
  return ret;
}
template <class T>
T extgcd(T a, T b, T& x, T& y) {
  for (T u = y = 1, v = x = 0; a;) {
    T q = b / a;
    swap(x -= q * u, u);
    swap(y -= q * v, v);
    swap(b -= q * a, a);
  }
  return b;
}
template <class T>
T mod_inv(T a, T m) {
  T x, y;
  extgcd(a, m, x, y);
  return (m + x % m) % m;
}
const int N = ((int)1e7) + 1;
bool prime[N];
vector<int> prs;
void init_prime() {
  memset(prime, 1, sizeof(prime));
  prime[0] = prime[1] = false;
  for (int i = 2; i < sizeof(prime); i++)
    if (prime[i])
      for (int j = i * 2; j < sizeof(prime); j += i) prime[j] = false;
  for (int i = 2; i < sizeof(prime); i++)
    if (prime[i]) prs.push_back(i);
}
int factors[N];
void init_factor() {
  for (int i = 2; i < N; i += 2) factors[i] = 2;
  for (int i = 3; i < N; i += 2) factors[i] = i;
  for (int i = 3; i < N; i += 2)
    if (factors[i] == i)
      for (int j = 3 * i; j < N; j += 2 * i) chmin(factors[j], i);
}
ll cnt1(int n) {
  ll ret = 0;
  static char di[((int)1e7) + 1];
  memset(di, 0, sizeof(char) * (n + 1));
  for (int i = 2; i <= n; i++) {
    int use = 1 - di[i];
    if (use == 0) continue;
    ll val = (n / i) * ll(n / i);
    ret += val * use;
    for (int j = i * 2; j <= n; j += i) {
      di[j] += use;
    }
  }
  int diagonal = n - 1;
  ret = (ret - diagonal) / 2;
  return ret;
}
ll solve(int n) {
  ll a = cnt1(n);
  ll b = 0;
  {
    static ll sm[((int)1e7) + 10];
    memset(sm, 0, sizeof(ll) * (n + 2));
    for (int i = 2; i <= n; i++) {
      sm[factors[i]]++;
    }
    sm[1] = 1;
    for (int i = 0; i < (n + 1); i++) sm[i + 1] += sm[i];
    for (int l = 0; l < (n); l++) {
      if (l <= 1) continue;
      const int rp = n / l;
      if (l >= rp) break;
      ll ccnt = sm[l] - sm[l - 1];
      ll rcnt = sm[rp] - sm[l];
      b += ccnt * rcnt;
    }
    for (int l = 0; l < (n); l++) {
      if (l <= 1) continue;
      ll ccnt = sm[l] - sm[l - 1];
      ll addd = ccnt * (ccnt - 1) / 2;
      b += addd;
    }
    b -= a;
  }
  ll dall = 0;
  {
    ll pcnt = 0;
    for (int i = n / 2 + 1; i <= n; i++)
      if (prime[i]) pcnt++;
    pcnt++;
    dall = (n - pcnt) * (n - pcnt - 1) / 2;
  }
  ll c = dall - a - b;
  return a + b * 2 + c * 3;
}
ll solve2(int n) {
  n++;
  static int di[1000][1000];
  memset(di, 0x1f, sizeof(di));
  for (int i = 0; i < (n); i++)
    for (int j = 0; j < (n); j++) {
      if (i == 0 || j == 0) continue;
      if (gcd(i, j) != 1) {
        di[i][j] = 1;
      }
    }
  for (int i = 0; i < (n); i++) di[i][i] = 0;
  for (int k = 0; k < (n); k++)
    for (int i = 0; i < (n); i++)
      for (int j = 0; j < (n); j++) chmin(di[i][j], di[i][k] + di[k][j]);
  ll ret = 0;
  int ec[4] = {};
  for (int i = 0; i < (n); i++)
    for (int j = i + 1; j < n; j++) {
      if (di[i][j] <= 10) {
        ret += di[i][j];
        if (di[i][j] >= 4) {
          cout << "?";
        }
        ec[di[i][j]]++;
        if (di[i][j] == 3) {
          printf("(%d, %d)\n", i, j);
        }
      }
    }
  writerArr(ec, 4);
  return ret;
}
void tst() {
  for (int i = 21; i <= 100; i++) {
    ll cur = solve(i);
    ll c2 = solve2(i);
    if (cur != c2) {
      cout << "?";
    }
    cout << cur << endl;
  }
}
int main() {
  init_prime();
  init_factor();
  int n;
  reader(n);
  cout << solve(n) << endl;
  return 0;
}

```