#include <bits/stdc++.h>
using namespace std;
const int maxN = 5e5 + 5;
const long long mod = 1e9 + 7;
long long power[maxN];
int n, a[maxN], b[maxN], cnt[maxN];
struct segTree {
long long st[maxN << 2], lz[maxN << 2];
void build(int id, int l, int r) {
lz[id] = 1;
if (l == r) {
st[id] = power[n];
return ;
}
int mid = (l + r) >> 1;
build(id << 1, l, mid);
build(id << 1 | 1, mid + 1, r);
st[id] = st[id << 1] + st[id << 1 | 1];
if (st[id] >= mod) st[id] -= mod;
}
void down(int id) {
st[id << 1] = (st[id << 1] * lz[id]) % mod;
st[id << 1 | 1] = (st[id << 1 | 1] * lz[id]) % mod;
lz[id << 1] = (lz[id << 1] * lz[id]) % mod;
lz[id << 1 | 1] = (lz[id << 1 | 1] * lz[id]) % mod;
lz[id] = 1;
}
void update(int id, int l, int r, int u, int v, long long val) {
if (v < l || r < u) return ;
if (u <= l && r <= v) {
if (st[id] == 0) return ;
st[id] = (st[id] * val) % mod;
lz[id] = (lz[id] * val) % mod;
return ;
}
if (lz[id] != 1) down(id);
int mid = (l + r) >> 1;
update(id << 1, l, mid, u, v, val);
update(id << 1 | 1, mid + 1, r, u, v, val);
st[id] = st[id << 1] + st[id << 1 | 1];
if (st[id] >= mod) st[id] -= mod;
}
} lt, rt;
bool cmp(pair<int, int> A, pair<int, int> B) {
return A.first > B.first;
}
vector<pair<int, int>> query;
int main() {
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n;
power[0] = 1;
for (int i = 1; i <= n; i++)
power[i] = (power[i - 1] + power[i - 1]) % mod;
for (int i = 1; i <= n; i++)
cin >> a[i];
for (int i = 1; i <= n; i++) {
cin >> b[i];
query.push_back({a[i], i});
query.push_back({b[i], i});
cnt[i] = 2;
}
sort(query.begin(), query.end(), cmp);
lt.build(1, 1, n);
rt.build(1, 1, n);
// cout << lt.st[1] << ' ' << rt.st[1] << '\n';
int pre = max(*max_element(a + 1, a + n + 1), *max_element(b + 1, b + n + 1));
long long ans = 0, empty_full = power[n], wall_blocked = 0, revPow = 500000004;
for (auto [layer, i]: query) {
// cout << "? " << layer << ' ' << i << '\n';
if (pre != layer) {
long long total = 1LL * n * power[n] % mod;
long long emptyLR = (lt.st[1] + rt.st[1] - 1LL * n * empty_full) % mod;
emptyLR += wall_blocked; if (emptyLR >= mod) emptyLR -= mod;
total = total - emptyLR; if (total < 0) total += mod;
ans = (ans + 1LL * (pre - layer) * total) % mod;
}
cnt[i]--;
long long update_mul = (cnt[i] == 1 ? revPow : 0);
lt.update(1, 1, n, i, n, update_mul);
rt.update(1, 1, n, n - i + 1, n, update_mul);
wall_blocked += power[n - 1];
if (wall_blocked >= mod) wall_blocked -= mod;
empty_full = (empty_full * update_mul) % mod;
pre = layer;
}
long long total = 1LL * n * power[n] % mod;
long long emptyLR = (lt.st[1] + rt.st[1] - 1LL * n * empty_full) % mod;
emptyLR += wall_blocked; if (emptyLR >= mod) emptyLR -= mod;
total = total - emptyLR; if (total < 0) total += mod;
ans = (ans + 1LL * (pre - 1) * total) % mod;
cout << ans << '\n';
return 0;
}
