timus1887

#pragma GCC optimize("Ofast")
#pragma GCC target("tune=native")
#pragma GCC optimize("fast-math,unroll-loops")

#include <math.h>
#include <algorithm>
#include <set>
#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <string>
#include <time.h>
#include <cassert>
#include <functional>
#include <memory.h>
#include <stack>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <chrono>
#include <complex>
#include <fstream>
#include <climits>
using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef unsigned u;
typedef long double ld;
typedef vector<vector<int>> vvi;
typedef unsigned char uc;
typedef unsigned short us;
typedef complex<double> cd;

#define INF 1000000000
#define LLINF 1000000000000000000LL
#define EPS 1e-9l
#define pii pair<int, int>

const int DEBUG = 0;

mt19937 gen((u)chrono::high_resolution_clock::now().time_since_epoch().count());

#pragma comment(linker, "/STACK:16777216")

const int ITER = 50000;

ld prob[26][11];
int a[26];
int b[26];
int c[26];
ld p[10];
ld dp[2][1 << 10];

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.setf(cout.fixed);
    cout.precision(12);
    auto START_TIME = chrono::high_resolution_clock::now();

    int n;
    cin >> n;

    for (int i = 1; i <= n; i++)
        cin >> a[i];

    for (int i = 1; i <= n; i++)
        cin >> b[i];

    for (int i = 1; i <= n; i++)
        cin >> c[i];

    prob[0][1] = 1;

    for (int len = 0; len < n; len++)
    {
        for (int mult = 0; mult < 11; mult++)
        {
            for (int dig = 0; dig < 10; dig++)
            {
                int add = (a[len + 1] * dig * dig + b[len + 1] * dig + c[len + 1]) % 11;
                add = (add * mult) % 11;

                prob[len + 1][add] += prob[len][mult] / 10;
            }
        }
    }

    for (int i = 0; i < 11; i++)
        p[i % 10] += prob[n][i];

    for (int i = 0; i < 10; i++)
    {
        if (p[i] < 1e-8)
        {
            cout << -1;
            return 0;
        }
    }

    dp[0][0] = 1;
    ld res = 0;

    for (int i = 0; i + 1 < ITER; i++)
    {
        res += i * dp[i % 2][(1 << 10) - 1];

        for (int mask = 0; mask < (1 << 10) - 1; mask++)
        {
            if (dp[i % 2][mask] > 1e-10)
            {
                for (int dig = 0; dig < 10; dig++)
                {
                    dp[(i + 1) % 2][mask | (1 << dig)] += dp[i % 2][mask] * p[dig];
                }
            }
        }

        fill(dp[i % 2], dp[i % 2] + (1 << 10), 0);
    }

    cout << res;

#ifdef LOCAL
    cerr.precision(3);
    cerr << "\nWorking time: " << chrono::duration<double>(chrono::high_resolution_clock::now() - START_TIME).count() << " sec.";
#endif

    return 0;
}