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
#include <bits/stdc++.h>
using namespace std;
const long long MAXN = 1e5 + 5;
const long long SQRTN = 1003;
const long long LOGN = 22;
const double PI = acos(-1);
const long long INF = 1e18;
const long long MOD = 1e9 + 7;
const long long FMOD = 998244353;
const double eps = 1e-9;
void __print(long long x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  long long f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
mt19937 RNG(chrono::steady_clock::now().time_since_epoch().count());
template <typename T>
T gcd(T a, T b) {
  if (b == 0) return a;
  a %= b;
  return gcd(b, a);
}
template <typename T>
T lcm(T a, T b) {
  return (a * (b / gcd(a, b)));
}
long long add(long long a, long long b, long long c = MOD) {
  long long res = a + b;
  return (res >= c ? res % c : res);
}
long long sub(long long a, long long b, long long c = MOD) {
  long long res;
  if (abs(a - b) < c)
    res = a - b;
  else
    res = (a - b) % c;
  return (res < 0 ? res + c : res);
}
long long mul(long long a, long long b, long long c = MOD) {
  long long res = (long long)a * b;
  return (res >= c ? res % c : res);
}
long long muln(long long a, long long b, long long c = MOD) {
  long long res = (long long)a * b;
  return ((res % c) + c) % c;
}
long long mulmod(long long a, long long b, long long m = MOD) {
  long long q = (long long)(((long double)a * (long double)b) / (long double)m);
  long long r = a * b - q * m;
  if (r > m) r %= m;
  if (r < 0) r += m;
  return r;
}
template <typename T>
T binpow(T e, T n) {
  T x = 1, p = e;
  while (n) {
    if (n & 1) x = x * p;
    p = p * p;
    n >>= 1;
  }
  return x;
}
template <typename T>
T binpow2(T e, T n, T m = MOD) {
  T x = 1, p = e;
  while (n) {
    if (n & 1) x = mul(x, p, m);
    p = mul(p, p, m);
    n >>= 1;
  }
  return x;
}
template <typename T>
T extended_euclid(T a, T b, T &x, T &y) {
  T xx = 0, yy = 1;
  y = 0;
  x = 1;
  while (b) {
    T q = a / b, t = b;
    b = a % b;
    a = t;
    t = xx;
    xx = x - q * xx;
    x = t;
    t = yy;
    yy = y - q * yy;
    y = t;
  }
  return a;
}
template <typename T>
T mod_inverse(T a, T n = MOD) {
  T x, y, z = 0;
  T d = extended_euclid(a, n, x, y);
  return (d > 1 ? -1 : sub(x, z, n));
}
const long long FACSZ = 1e4;
long long fact[FACSZ], ifact[FACSZ];
void precom(long long c = MOD) {
  fact[0] = 1;
  for (long long i = 1; i < FACSZ; i++) fact[i] = mul(fact[i - 1], i, c);
  ifact[FACSZ - 1] = mod_inverse(fact[FACSZ - 1], c);
  for (long long i = FACSZ - 1 - 1; i >= 0; i--) {
    ifact[i] = mul(i + 1, ifact[i + 1], c);
  }
}
vector<long long> primes;
void prime_precom() {
  primes.push_back(2);
  for (long long x = 3; primes.size() <= MAXN; x += 2) {
    bool isPrime = true;
    for (auto p : primes) {
      if (x % p == 0) {
        isPrime = false;
        break;
      }
      if (p * p > x) {
        break;
      }
    }
    if (isPrime) {
      primes.push_back(x);
    }
  }
}
long long ncr(long long n, long long k) {
  if (n < k) return 0;
  if (k == 0) return 1;
  long long res = 1;
  if (k > n - k) k = n - k;
  for (long long i = 0; i < k; ++i) {
    res *= (n - i);
    res /= (i + 1);
  }
  return res;
}
long long ncr_modp(long long n, long long k, long long c = MOD) {
  if (n < k) return 0;
  if (k == 0) return 1;
  long long res = 1;
  if (k > n - k) k = n - k;
  for (long long i = 0; i < k; ++i) {
    res = mul(res, n - i, c);
    res = mul(res, binpow2(i + 1, c - 2, c), c);
  }
  return res;
}
vector<long long> factors;
void factorize(long long a) {
  factors.clear();
  for (long long i = 1; i * i <= a; i++) {
    if (a % i == 0) {
      factors.push_back(i);
      factors.push_back(a / i);
    }
  }
  sort(factors.begin(), factors.end());
}
long long ncr_precom(long long n, long long r, long long c = MOD) {
  return mul(mul(ifact[r], ifact[n - r], c), fact[n], c);
}
long long ceil(long long a, long long b) { return (a + b - 1) / b; }
bool is_prime(long long n) {
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      return 0;
    }
  }
  return 1;
}
bool diophantine_checker(long long a, long long b, long long n) {
  for (long long i = 0; i * a <= n; i++) {
    if ((n - (i * a)) % b == 0) {
      return true;
    }
  }
  return false;
}
long long count_divisors(long long n) {
  long long c;
  long long ans = 1;
  for (long long i = 2; i * i <= n; i++) {
    c = 0;
    while (n % i == 0) {
      c++;
      n /= i;
    }
    ans *= (c + 1);
  }
  if (n > 2) {
    return ans * 2;
  }
  return ans;
}
string to_binary(long long n) {
  string r;
  while (n != 0) {
    r = (n % 2 == 0 ? "0" : "1") + r;
    n /= 2;
  }
  return r;
}
bool ispower2(long long x) { return x && (!(x & (x - 1))); }
vector<long long> spf;
void sieve() {
  spf.resize(MAXN);
  spf[1] = 1;
  for (long long i = 2; i < MAXN; i++) {
    spf[i] = i;
  }
  for (long long i = 4; i < MAXN; i += 2) {
    spf[i] = 2;
  }
  for (long long i = 3; i * i <= MAXN; i++) {
    if (spf[i] == i) {
      for (long long j = i * i; j < MAXN; j += i) {
        if (spf[j] == j) {
          spf[j] = i;
        }
      }
    }
  }
}
void pfactor(long long x, vector<long long> &ret) {
  while (x != 1) {
    ret.push_back(spf[x]);
    x = x / spf[x];
  }
}
vector<long long> phi;
void phi_1_to_n(long long n) {
  phi.resize(n + 1);
  phi[0] = 0;
  phi[1] = 1;
  for (long long i = 2; i <= n; i++) phi[i] = i;
  for (long long i = 2; i <= n; i++) {
    if (phi[i] == i) {
      for (long long j = i; j <= n; j += i) phi[j] -= phi[j] / i;
    }
  }
}
vector<long long> fac[MAXN];
long long cal(vector<long long> &cur) {
  long long sm = 0;
  map<long long, long long> make_pair;
  for (auto z : cur) {
    for (auto p : fac[z]) {
      make_pair[p]++;
    }
  }
  for (auto z : make_pair) {
    sm += z.second * z.second * phi[z.first];
  }
  return sm;
}
void solvethetestcase() {
  long long n;
  cin >> n;
  vector<long long> v(n + 1);
  for (long long i = 0; i < n; i++) {
    cin >> v[i + 1];
  }
  phi_1_to_n(MAXN);
  for (long long i = 1; i < MAXN; i++) {
    for (long long j = i; j < MAXN; j += i) {
      fac[j].push_back(i);
    }
  }
  long long ans = 0;
  for (long long x = 1; x <= n; x++) {
    vector<long long> cur;
    for (long long i = x; i <= n; i += x) {
      cur.push_back(v[i]);
    }
    ans += cal(cur) * phi[x];
  }
  cout << ans << "\n";
}
signed main() {
  cout << fixed << setprecision(12);
  ;
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  for (long long testcase = 1; testcase < t + 1; testcase++) {
    solvethetestcase();
  }
}
