#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 7;
const int mod = 1e9 + 7;
int phi[N];
int check[N];
int a[N];
vector<int> v[N];
int cnt[N], prime[N];
void init() {
  phi[1] = 1;
  check[0] = 1;
  for (int i = 1; i < N; i++)
    for (int j = i; j < N; j += i) {
      v[j].push_back(i);
    }
  for (int i = 2; i < N; i++) {
    if (!check[i]) {
      prime[++prime[0]] = i;
      phi[i] = i - 1;
    }
    for (int j = 1; j <= prime[0]; j++) {
      if ((long long)i * prime[j] >= N) break;
      check[i * prime[j]] = 1;
      if (i % prime[j] == 0) {
        phi[i * prime[j]] = phi[i] * prime[j];
        break;
      } else {
        phi[i * prime[j]] = phi[i] * phi[prime[j]];
      }
    }
  }
}
int main() {
  init();
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    vector<int> vv;
    for (int j = i; j <= n; j += i) {
      for (int d : v[a[j]]) {
        vv.push_back(d);
        cnt[d]++;
      }
    }
    long long tmp = 0;
    for (int d : vv) {
      tmp = (tmp + (((long long)cnt[d] * cnt[d] * phi[d]) % mod)) % mod;
      cnt[d] = 0;
    }
    ans = (ans + tmp * phi[i] % mod) % mod;
  }
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Generate a cpp solution to the following problem:

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 + 7;
const int mod = 1e9 + 7;
int phi[N];
int check[N];
int a[N];
vector<int> v[N];
int cnt[N], prime[N];
void init() {
  phi[1] = 1;
  check[0] = 1;
  for (int i = 1; i < N; i++)
    for (int j = i; j < N; j += i) {
      v[j].push_back(i);
    }
  for (int i = 2; i < N; i++) {
    if (!check[i]) {
      prime[++prime[0]] = i;
      phi[i] = i - 1;
    }
    for (int j = 1; j <= prime[0]; j++) {
      if ((long long)i * prime[j] >= N) break;
      check[i * prime[j]] = 1;
      if (i % prime[j] == 0) {
        phi[i * prime[j]] = phi[i] * prime[j];
        break;
      } else {
        phi[i * prime[j]] = phi[i] * phi[prime[j]];
      }
    }
  }
}
int main() {
  init();
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    vector<int> vv;
    for (int j = i; j <= n; j += i) {
      for (int d : v[a[j]]) {
        vv.push_back(d);
        cnt[d]++;
      }
    }
    long long tmp = 0;
    for (int d : vv) {
      tmp = (tmp + (((long long)cnt[d] * cnt[d] * phi[d]) % mod)) % mod;
      cnt[d] = 0;
    }
    ans = (ans + tmp * phi[i] % mod) % mod;
  }
  printf("%lld\n", ans);
  return 0;
}

```