#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
const int mod = 1e9 + 7;
int n;
unordered_map<int, int> mp;
int phi[maxn];
vector<int> num1[maxn];
vector<int> num2;
int mul(int a, int b, int p) {
  int ans = 0;
  for (; b; b >>= 1, a = (a + a) % p)
    if (b & 1) ans = (ans + a) % p;
  return ans;
}
void phi_table(int n) {
  phi[1] = 1;
  for (int i = 2; i <= n; i++)
    if (!phi[i]) {
      for (int j = i; j <= n; j += i) {
        if (!phi[j]) phi[j] = j;
        phi[j] = phi[j] / i * (i - 1);
      }
    }
}
void init() {
  phi_table(maxn - 1);
  for (int i = 1; i < maxn; i++) {
    for (int j = i; j < maxn; j += i) {
      num1[j].push_back(i);
    }
  }
  int temp;
  num2.push_back(0);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &temp);
    num2.push_back(temp);
  }
}
void solve() {
  int ans = 0;
  for (int d = 1; d <= n; d++) {
    int tmp = 0;
    mp.clear();
    for (int i = 1; i <= n / d; i++) {
      for (auto it : num1[num2[i * d]]) {
        mp[it]++;
      }
    }
    for (auto it : mp) {
      tmp =
          (tmp + mul(phi[it.first], mul(it.second, it.second, mod), mod)) % mod;
    }
    ans = (ans + mul(phi[d], tmp, mod)) % mod;
  }
  printf("%d\n", ans);
}
signed main() {
  scanf("%d", &n);
  init();
  solve();
}

### Prompt

Your challenge is to write 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 maxn = 1e5 + 10;
const int mod = 1e9 + 7;
int n;
unordered_map<int, int> mp;
int phi[maxn];
vector<int> num1[maxn];
vector<int> num2;
int mul(int a, int b, int p) {
  int ans = 0;
  for (; b; b >>= 1, a = (a + a) % p)
    if (b & 1) ans = (ans + a) % p;
  return ans;
}
void phi_table(int n) {
  phi[1] = 1;
  for (int i = 2; i <= n; i++)
    if (!phi[i]) {
      for (int j = i; j <= n; j += i) {
        if (!phi[j]) phi[j] = j;
        phi[j] = phi[j] / i * (i - 1);
      }
    }
}
void init() {
  phi_table(maxn - 1);
  for (int i = 1; i < maxn; i++) {
    for (int j = i; j < maxn; j += i) {
      num1[j].push_back(i);
    }
  }
  int temp;
  num2.push_back(0);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &temp);
    num2.push_back(temp);
  }
}
void solve() {
  int ans = 0;
  for (int d = 1; d <= n; d++) {
    int tmp = 0;
    mp.clear();
    for (int i = 1; i <= n / d; i++) {
      for (auto it : num1[num2[i * d]]) {
        mp[it]++;
      }
    }
    for (auto it : mp) {
      tmp =
          (tmp + mul(phi[it.first], mul(it.second, it.second, mod), mod)) % mod;
    }
    ans = (ans + mul(phi[d], tmp, mod)) % mod;
  }
  printf("%d\n", ans);
}
signed main() {
  scanf("%d", &n);
  init();
  solve();
}

```