#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5, mod = 1e9 + 7;
int n, a[N], phi[N], cnt[N];
vector<int> d[N];
void init() {
  for (int i = 1; i < (N); ++i) {
    phi[i] = i;
  }
  for (int i = 2; i < (N); ++i) {
    if (phi[i] == i) {
      for (int j = i; j < N; j += i) {
        phi[j] -= phi[j] / i;
      }
    }
  }
  for (int i = 1; i < (N); ++i) {
    for (int j = i; j < N; j += i) {
      d[j].push_back(i);
    }
  }
}
int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  init();
  cin >> n;
  for (int i = 1; i < (n + 1); ++i) {
    cin >> a[i];
  }
  long long ans = 0;
  for (int x = 1; x < (n + 1); ++x) {
    for (int i = x; i <= n; i += x) {
      for (const int j : d[a[i]]) {
        ++cnt[j];
      }
    }
    for (int i = x; i <= n; i += x) {
      for (const int j : d[a[i]]) {
        if (cnt[j]) {
          ans = (ans +
                 phi[x] * 1ll * phi[j] % mod * cnt[j] % mod * cnt[j] % mod) %
                mod;
          cnt[j] = 0;
        }
      }
    }
  }
  cout << ans << '\n';
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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 N = 1e5 + 5, mod = 1e9 + 7;
int n, a[N], phi[N], cnt[N];
vector<int> d[N];
void init() {
  for (int i = 1; i < (N); ++i) {
    phi[i] = i;
  }
  for (int i = 2; i < (N); ++i) {
    if (phi[i] == i) {
      for (int j = i; j < N; j += i) {
        phi[j] -= phi[j] / i;
      }
    }
  }
  for (int i = 1; i < (N); ++i) {
    for (int j = i; j < N; j += i) {
      d[j].push_back(i);
    }
  }
}
int main() {
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  init();
  cin >> n;
  for (int i = 1; i < (n + 1); ++i) {
    cin >> a[i];
  }
  long long ans = 0;
  for (int x = 1; x < (n + 1); ++x) {
    for (int i = x; i <= n; i += x) {
      for (const int j : d[a[i]]) {
        ++cnt[j];
      }
    }
    for (int i = x; i <= n; i += x) {
      for (const int j : d[a[i]]) {
        if (cnt[j]) {
          ans = (ans +
                 phi[x] * 1ll * phi[j] % mod * cnt[j] % mod * cnt[j] % mod) %
                mod;
          cnt[j] = 0;
        }
      }
    }
  }
  cout << ans << '\n';
}

```