#include <bits/stdc++.h>
using namespace std;
const int _ = 1e5 + 7, P = 1e9 + 7;
int N, A[_], prm[_], cprm, phi[_], cnt[_];
bool nprm[_];
vector<int> lst[_];
void sieve() {
  phi[1] = 1;
  for (int i = 2; i <= 1e5; ++i) {
    if (!nprm[i]) {
      prm[++cprm] = i;
      phi[i] = i - 1;
    }
    for (int j = 1; prm[j] * i <= 1e5; ++j) {
      nprm[prm[j] * i] = 1;
      if (i % prm[j] == 0) {
        phi[i * prm[j]] = phi[i] * prm[j];
        break;
      }
      phi[i * prm[j]] = phi[i] * (prm[j] - 1);
    }
  }
  for (int i = 1; i <= 1e5; ++i)
    for (int j = i; j <= 1e5; j += i) lst[j].push_back(i);
}
int main() {
  ios::sync_with_stdio(0);
  sieve();
  cin >> N;
  for (int i = 1; i <= N; ++i) cin >> A[i];
  int ans = 0;
  vector<int> vis;
  for (int d = 1; d <= N; ++d) {
    for (int t = d; t <= N; t += d)
      for (auto v : lst[A[t]])
        if (!(cnt[v]++)) vis.push_back(v);
    for (auto t : vis) {
      ans = (ans + 1ll * phi[d] * phi[t] % P * cnt[t] * cnt[t]) % P;
      cnt[t] = 0;
    }
    vis.clear();
  }
  cout << ans;
  return 0;
}

### 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;
const int _ = 1e5 + 7, P = 1e9 + 7;
int N, A[_], prm[_], cprm, phi[_], cnt[_];
bool nprm[_];
vector<int> lst[_];
void sieve() {
  phi[1] = 1;
  for (int i = 2; i <= 1e5; ++i) {
    if (!nprm[i]) {
      prm[++cprm] = i;
      phi[i] = i - 1;
    }
    for (int j = 1; prm[j] * i <= 1e5; ++j) {
      nprm[prm[j] * i] = 1;
      if (i % prm[j] == 0) {
        phi[i * prm[j]] = phi[i] * prm[j];
        break;
      }
      phi[i * prm[j]] = phi[i] * (prm[j] - 1);
    }
  }
  for (int i = 1; i <= 1e5; ++i)
    for (int j = i; j <= 1e5; j += i) lst[j].push_back(i);
}
int main() {
  ios::sync_with_stdio(0);
  sieve();
  cin >> N;
  for (int i = 1; i <= N; ++i) cin >> A[i];
  int ans = 0;
  vector<int> vis;
  for (int d = 1; d <= N; ++d) {
    for (int t = d; t <= N; t += d)
      for (auto v : lst[A[t]])
        if (!(cnt[v]++)) vis.push_back(v);
    for (auto t : vis) {
      ans = (ans + 1ll * phi[d] * phi[t] % P * cnt[t] * cnt[t]) % P;
      cnt[t] = 0;
    }
    vis.clear();
  }
  cout << ans;
  return 0;
}

```