#pragma GCC optimize(2)

#pragma GCC optimize(3)

#pragma GCC optimize(4)

#include<bits/stdc++.h>

using namespace std;

#define y1 y11

#define fi first

#define se second

#define pi acos(-1.0)

#define LL long long

//#define mp make_pair

#define pb push_back

#define ls rt<<1, l, m

#define rs rt<<1|1, m+1, r

#define ULL unsigned LL

#define pll pair<LL, LL>

#define pli pair<LL, int>

#define pii pair<int, int>

#define piii pair<pii, int>

#define pdd pair<double, double>

#define mem(a, b) memset(a, b, sizeof(a))

#define debug(x) cerr << #x << " = " << x << "\n";

#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);

//head

const int MOD = 1e9 + ;

const int N = 2e5 + ;

int l[N], r[N], n;

LL p[N], q[N], sum[N];

LL q_pow(LL n, LL k) {

    LL res = ;

    while(k) {

        if(k&) res = (res * n) % MOD;

        n = (n * n) % MOD;

        k >>= ;

    }

    return res;

}

int main() {

    scanf("%d", &n);

    for (int i = ; i <= n; ++i) scanf("%d", &l[i]);

    for (int i = ; i <= n; ++i) scanf("%d", &r[i]);

    for (int i = ; i <= n; ++i) {

        int L = max(l[i-], l[i]), R = min(r[i-], r[i]);

        if(L > R) p[i] = , q[i] = ;

        else q[i] = (R-L+)*q_pow((r[i]-l[i]+)*1LL*(r[i-]-l[i-]+)%MOD, MOD-)%MOD, p[i] = (-q[i]+MOD)%MOD;

        sum[i] = (sum[i-] + p[i]) % MOD;

    }

    LL ans = sum[n];

    for (int i = ; i <= n ;++i) {

        LL tot = sum[n];

        tot = (tot - p[i])%MOD;

        if(i- >= ) tot = (tot - p[i-]) % MOD;

        if(i+ <= n) tot = (tot - p[i+]) % MOD;

        tot = (tot + MOD) % MOD;

        ans = (ans + p[i]*tot%MOD) % MOD;

    }

    for (int i = ; i < n; ++i) {

        LL tot = ((-q[i]-q[i+])%MOD+MOD)%MOD;

        if(i- >= ) {

            int L = max(l[i-], max(l[i], l[i+])), R= min(r[i-], min(r[i], r[i+]));

            if(L <= R)tot = (tot + (R-L+)*q_pow((r[i]-l[i]+)*1LL*(r[i-]-l[i-]+)%MOD*(r[i+]-l[i+]+)%MOD, MOD-)%MOD)%MOD;

        }

        ans = (ans + *tot) % MOD;

    }

    printf("%lld\n", ans%MOD);

    return ;

}