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
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define endl "\n"
typedef pair<int, int> Pii;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(s) (s).begin(),(s).end()
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define pb push_back
#define P pair<ll,ll>
#define PQminll priority_queue<ll, vector<ll>, greater<ll>>
#define PQmaxll priority_queue<ll,vector<ll>,less<ll>>
#define PQminP priority_queue<P, vector<P>, greater<P>>
#define PQmaxP priority_queue<P,vector<P>,less<P>>
#define NP next_permutation
//const ll mod = 1000000009;
//const ll mod = 998244353;
const ll mod = 1000000007;
const ll inf = 4100000000000000000ll;
const ld eps = ld(0.00000000001);
//static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T,class K>void vcin(vector<T> &n,vector<K> &m){for(int i=0;i<int(n.size());i++) cin>>n[i]>>m[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
template<class T>void vcin(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cin>>n[i][j];}}}
template<class T>void vcout(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cout<<n[i][j]<<" ";}cout<<endl;}cout<<endl;}
void yes(bool a){cout<<(a?"yes":"no")<<endl;}
void YES(bool a){cout<<(a?"YES":"NO")<<endl;}
void Yes(bool a){cout<<(a?"Yes":"No")<<endl;}
void possible(bool a){ cout<<(a?"possible":"impossible")<<endl; }
void Possible(bool a){ cout<<(a?"Possible":"Impossible")<<endl; }
void POSSIBLE(bool a){ cout<<(a?"POSSIBLE":"IMPOSSIBLE")<<endl; }
template<class T>auto min(const T& a){ return *min_element(all(a)); }
template<class T>auto max(const T& a){ return *max_element(all(a)); }
template<class T,class F>void print(pair<T,F> a){cout<<a.fi<<" "<<a.se<<endl;}
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0;}
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
ll fastgcd(ll u,ll v){ll shl=0;while(u&&v&&u!=v){bool eu=!(u&1);bool ev=!(v&1);if(eu&&ev){++shl;u>>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<<shl:u<<shl;}
ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
vector<ll> divisor(ll x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; }
ll pop(ll x){return __builtin_popcountll(x);}
ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;}
P hyou(P a){ll x=fastgcd(abs(a.fi),abs(a.se));a.fi/=x;a.se/=x;if(a.se<0){a.fi*=-1;a.se*=-1;}return a;}
P Pplus(P a,P b){ return hyou({a.fi*b.se+b.fi*a.se,a.se*b.se});}
P Ptimes(P a,ll b){ return hyou({a.fi*b,a.se});}
P Ptimes(P a,P b){ return hyou({a.fi*b.fi,a.se*b.se});}
P Pminus(P a,P b){ return hyou({a.fi*b.se-b.fi*a.se,a.se*b.se});}
P Pgyaku(P a){ return hyou({a.se,a.fi});}
template<class T>
struct Sum{
  vector<T> data;
  Sum(const vector<T>& v):data(v.size()+1){
    for(ll i=0;i<v.size();i++) data[i+1]=data[i]+v[i];
  }
  T get(ll l,ll r) const {
    return data[r]-data[l];
  }
};
template<class T>
struct Sum2{
  vector<vector<T>> data;
  Sum2(const vector<vector<T>> &v):data(v.size()+1,vector<T>(v[0].size()+1)){
    for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]=data[i][j+1]+v[i][j];
    for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]+=data[i+1][j];
  }
  T get(ll x1,ll y1,ll x2,ll y2) const {
    return data[x2][y2]+data[x1][y1]-data[x1][y2]-data[x2][y1];
  }
};

void cincout(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(20);
}
vector<vector<ll>> h;
ll solve(vector<ll> a){
  if(a.size()>=600){
    ll t=100000;
    vector<ll> now(t+1);
    for(auto e:a) now[e]++;
    for(int i=1;i<=t;i++){
      for(int j=2*i;j<=t;j+=i) now[i]+=now[j];
    }
    for(int i=1;i<=t;i++) (now[i]*=now[i])%=mod;;
    for(int i=t;i>=1;i--){
        for(int j=2*i;j<=t;j+=i){
            now[i]+=mod-now[j];
            if(now[i]>=mod) now[i]-=mod;
        }
    }
    ll ans=0;
    for(ll i=1;i<=t;i++) (ans+=now[i]*i)%=mod;
    return ans;
  }
  else{
    ll sum=0;
    for(int i=0;i<a.size();i++){
        for(int j=i+1;j<a.size();j++){
            (sum+=2*gcd(a[i],a[j]));
            if(sum>=mod) sum-=mod;
        }
    }
    for(int i=0;i<a.size();i++){
        sum+=2*a[i];
        if(sum>=mod) sum-=mod;
    }
    return sum;
  }
}
int main() {
  cincout();
  ll n;
  cin>>n;
  h.resize(100001);
  for(int i=1;i<=100000;i++){
    for(int j=2*i;j<=100000;j+=i) h[j].pb(i);
  }
  vector<ll> a(n);
  vcin(a);
  vector<vector<ll>> d(n+1);
  for(int i=1;i<=n;i++){
    for(int j=i;j<=n;j+=i) d[i].pb(a[j-1]);
  }
  vector<ll> g(n+1);
  for(int i=1;i<=n;i++) g[i]=solve(d[i]);
  for(int i=n;i>=1;i--){
    for(auto e:h[i]) (g[e]+=mod-g[i])%=mod;
  }
  ll ans=0;
  for(int i=1;i<=n;i++) (ans+=(g[i]*ll(i))%mod)%=mod;
  cout<<ans<<endl;
}