All_Numbers.cpp

#include<bits/stdc++.h>
using namespace std;
#define int long long
#define all(x) (x).begin(),(x).end()
#define sz(x) (int)(x).size()
const long double EPS = 1e-14;
const int maxn = 100500;
const int mod = 1e9 + 7;
int pw[101];

struct Math{
    private: long long f[maxn];
    public:
    Math(){f[0] = 0;};
    long long add(long long x, long long y) { 
        x += y;
        if(x >= mod) x -= mod;
        if(x < 0) x += mod;
        return x;
    }
    long long mul(long long x, long long y) { return (add(x, mod) * add(y, mod)) % mod; }
    long long fast_pow(long long n, long long k){
            if(k == 0) return 1LL;
            long long ans = fast_pow(n, k >> 1);
            ans = mul(ans, ans);
            if(k & 1) ans = mul(n, ans);
            return ans;
    }
    long long inv(long long x) { return fast_pow(x, mod - 2); }
    void init_fact(){
        f[0] = 1LL;
        for(int i = 1 ; i < maxn ; ++i)
            f[i] = mul(i, f[i - 1]);
    }
    long long fact(int x){
        assert(x >= 0 && x < maxn);
        if(!f[0]) init_fact();
        return f[x];
    };
}math;

int calc(map < int, int > cnt, int n){
    int ans = 0;
    for(auto x : cnt){
        if(!x.second) continue;
        int size = math.fact(n - 1);
        for(auto y : cnt)
            size = math.mul(size, math.inv(math.fact(y.second - (y == x))));
        for(int i = 0 ; i < n ; ++i)
            ans = math.add(ans, math.mul(math.mul(x.first, pw[i]), size));
    }
    return ans;
}

signed main(){
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int n;
    cin >> n;
    pw[0] = 1;
    for(int i = 1 ; i < n + 5 ; ++i)
        pw[i] = math.mul(pw[i - 1], 10);
    map < int, int > cnt;
    for(int i = 0 ; i < n ; ++i){
        int x;
        cin >> x;
        cnt[x]++;
    }
    int ans = calc(cnt, n);
    if(cnt.count(0)){
        cnt[0]--;
        ans = math.add(ans, -calc(cnt, n - 1));
    }
    cout << ans << '\n';
    return 0;
}