#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
bool chmax(T &x, const T &y) {
  return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
  return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
  return (x >> i) & 1;
}
template <typename T>
void print(const vector<T> &v, T x = 0) {
  int n = v.size();
  for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
  int n = v.size();
  for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
  return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
  return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
  sort(begin(v), end(v));
  v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
  int n = v.size();
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  sort(begin(ret), end(ret),
       [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
  return ret;
}
struct io_setup {
  io_setup() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout << fixed << setprecision(15);
  }
} io_setup;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
const int MOD = 1000000007;
template <int mod>
struct Mod_Int {
  int x;
  Mod_Int() : x(0) {}
  Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  static int get_mod() { return mod; }
  Mod_Int &operator+=(const Mod_Int &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  Mod_Int &operator-=(const Mod_Int &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  Mod_Int &operator*=(const Mod_Int &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  Mod_Int &operator/=(const Mod_Int &p) {
    *this *= p.inverse();
    return *this;
  }
  Mod_Int &operator++() { return *this += Mod_Int(1); }
  Mod_Int operator++(int) {
    Mod_Int tmp = *this;
    ++*this;
    return tmp;
  }
  Mod_Int &operator--() { return *this -= Mod_Int(1); }
  Mod_Int operator--(int) {
    Mod_Int tmp = *this;
    --*this;
    return tmp;
  }
  Mod_Int operator-() const { return Mod_Int(-x); }
  Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
  Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
  Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
  Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
  bool operator==(const Mod_Int &p) const { return x == p.x; }
  bool operator!=(const Mod_Int &p) const { return x != p.x; }
  Mod_Int inverse() const {
    assert(*this != Mod_Int(0));
    return pow(mod - 2);
  }
  Mod_Int pow(long long k) const {
    Mod_Int now = *this, ret = 1;
    for (; k > 0; k >>= 1, now *= now) {
      if (k & 1) ret *= now;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const Mod_Int &p) {
    return os << p.x;
  }
  friend istream &operator>>(istream &is, Mod_Int &p) {
    long long a;
    is >> a;
    p = Mod_Int<mod>(a);
    return is;
  }
};
using mint = Mod_Int<MOD>;
int main() {
  int N;
  cin >> N;
  vector<int> a(N);
  for (int i = 0; i < N; i++) cin >> a[i];
  int M = 100000;
  vector<vector<int>> ds(M + 1);
  vector<ll> c(M + 1);
  iota(c.begin(), c.end(), 0);
  for (int i = 1; i <= M; i++) {
    ds[i].emplace_back(i);
    for (int j = 2 * i; j <= M; j += i) {
      c[j] -= c[i];
      ds[j].emplace_back(i);
    }
  }
  mint ans = 0;
  vector<ll> cnt(M + 1, 0);
  vector<bool> used(M + 1, false);
  for (int i = 1; i <= N; i++) {
    mint tmp = 0;
    for (int j = i - 1; j < N; j += i) {
      for (auto &e : ds[a[j]]) {
        used[e] = true;
        cnt[e]++;
      }
    }
    for (int j = i - 1; j < N; j += i) {
      for (auto &e : ds[a[j]]) {
        if (used[e]) {
          used[e] = false;
          tmp += c[e] * cnt[e] * cnt[e];
        }
        cnt[e]--;
      }
    }
    ans += tmp * c[i];
  }
  cout << ans << '\n';
}

### Prompt

Construct a cpp code solution to the problem outlined:

Mr. Chanek has an array a of n integers. The prettiness value of a is denoted as:

$$$∑_{i=1}^{n} {∑_{j=1}^{n} {\gcd(a_i, a_j) ⋅ \gcd(i, j)}}$$$

where \gcd(x, y) denotes the greatest common divisor (GCD) of integers x and y.

In other words, the prettiness value of an array a is the total sum of \gcd(a_i, a_j) ⋅ \gcd(i, j) for all pairs (i, j).

Help Mr. Chanek find the prettiness value of a, and output the result modulo 10^9 + 7!

Input

The first line contains an integer n (2 ≤ n ≤ 10^5).

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^5).

Output

Output an integer denoting the prettiness value of a modulo 10^9 + 7.

Example

Input


5
3 6 2 1 4


Output


77

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
bool chmax(T &x, const T &y) {
  return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
  return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
  return (x >> i) & 1;
}
template <typename T>
void print(const vector<T> &v, T x = 0) {
  int n = v.size();
  for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
  int n = v.size();
  for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
  return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
  return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
  sort(begin(v), end(v));
  v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
  int n = v.size();
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  sort(begin(ret), end(ret),
       [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
  return ret;
}
struct io_setup {
  io_setup() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout << fixed << setprecision(15);
  }
} io_setup;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
const int MOD = 1000000007;
template <int mod>
struct Mod_Int {
  int x;
  Mod_Int() : x(0) {}
  Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  static int get_mod() { return mod; }
  Mod_Int &operator+=(const Mod_Int &p) {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  Mod_Int &operator-=(const Mod_Int &p) {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  Mod_Int &operator*=(const Mod_Int &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  Mod_Int &operator/=(const Mod_Int &p) {
    *this *= p.inverse();
    return *this;
  }
  Mod_Int &operator++() { return *this += Mod_Int(1); }
  Mod_Int operator++(int) {
    Mod_Int tmp = *this;
    ++*this;
    return tmp;
  }
  Mod_Int &operator--() { return *this -= Mod_Int(1); }
  Mod_Int operator--(int) {
    Mod_Int tmp = *this;
    --*this;
    return tmp;
  }
  Mod_Int operator-() const { return Mod_Int(-x); }
  Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
  Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
  Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
  Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
  bool operator==(const Mod_Int &p) const { return x == p.x; }
  bool operator!=(const Mod_Int &p) const { return x != p.x; }
  Mod_Int inverse() const {
    assert(*this != Mod_Int(0));
    return pow(mod - 2);
  }
  Mod_Int pow(long long k) const {
    Mod_Int now = *this, ret = 1;
    for (; k > 0; k >>= 1, now *= now) {
      if (k & 1) ret *= now;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const Mod_Int &p) {
    return os << p.x;
  }
  friend istream &operator>>(istream &is, Mod_Int &p) {
    long long a;
    is >> a;
    p = Mod_Int<mod>(a);
    return is;
  }
};
using mint = Mod_Int<MOD>;
int main() {
  int N;
  cin >> N;
  vector<int> a(N);
  for (int i = 0; i < N; i++) cin >> a[i];
  int M = 100000;
  vector<vector<int>> ds(M + 1);
  vector<ll> c(M + 1);
  iota(c.begin(), c.end(), 0);
  for (int i = 1; i <= M; i++) {
    ds[i].emplace_back(i);
    for (int j = 2 * i; j <= M; j += i) {
      c[j] -= c[i];
      ds[j].emplace_back(i);
    }
  }
  mint ans = 0;
  vector<ll> cnt(M + 1, 0);
  vector<bool> used(M + 1, false);
  for (int i = 1; i <= N; i++) {
    mint tmp = 0;
    for (int j = i - 1; j < N; j += i) {
      for (auto &e : ds[a[j]]) {
        used[e] = true;
        cnt[e]++;
      }
    }
    for (int j = i - 1; j < N; j += i) {
      for (auto &e : ds[a[j]]) {
        if (used[e]) {
          used[e] = false;
          tmp += c[e] * cnt[e] * cnt[e];
        }
        cnt[e]--;
      }
    }
    ans += tmp * c[i];
  }
  cout << ans << '\n';
}

```