#include <bits/stdc++.h>
using namespace std;
int a[500005];
int b[500005];
const int MOD = 1e9 + 7;
vector<int> compressor_a, compressor_b;
class QueryMaintainer {
public:
int *FTmn;
int *FTmx;
int sz;
QueryMaintainer() {
sz = 0;
FTmn = new int[compressor_a.size() + 2];
memset(FTmn, 0, (compressor_a.size() + 2) * 4);
FTmx = new int[compressor_b.size() + 2];
memset(FTmx, 0, (compressor_b.size() + 2) * 4);
pridx_a = pridx_b = 0;
}
~QueryMaintainer() {
delete[] FTmn;
delete[] FTmx;
}
void mn_add(int idx, int amt) {
while (idx <= compressor_a.size() + 1) {
FTmn[idx] += amt;
idx++;
}
}
inline int mn_sum(const int &idx) { return FTmn[idx]; }
void mx_add(int idx, int amt) {
while (idx <= compressor_b.size() + 1) {
FTmx[idx] += amt;
idx++;
}
}
inline int mx_sum(const int &idx) { return FTmx[idx]; }
void insert(int a, int b) {
sz++;
mn_add(full_cpa(a) + 1, 1);
mx_add(full_cpb(b) + 1, 1);
}
void erase(int a, int b) {
sz--;
mn_add(full_cpa(a) + 1, -1);
mx_add(full_cpb(b) + 1, -1);
}
int pridx_a, pridx_b;
inline int full_cpa(const int &p) {
return lower_bound(compressor_a.begin(), compressor_a.end(), p) -
compressor_a.begin();
}
inline int full_cpb(const int &p) {
return lower_bound(compressor_b.begin(), compressor_b.end(), p) -
compressor_b.begin();
}
inline int cpa(const int &p) {
while (pridx_a < compressor_a.size() && compressor_a[pridx_a] < p)
pridx_a++;
return pridx_a;
}
inline int cpb(const int &p) {
while (pridx_b < compressor_b.size() && compressor_b[pridx_b] < p)
pridx_b++;
return pridx_b;
}
};
int pow2[500005];
inline int fastmod(const int &a) { return a >= MOD ? a - MOD : a; }
int solve_exact(int n) {
int ans = 0;
QueryMaintainer pref, suff;
for (int i = 0; i < n; i++)
suff.insert(a[i], b[i]);
set<int> possible;
for (int i = 0; i < n; i++) {
possible.insert(a[i]);
possible.insert(b[i]);
suff.erase(a[i], b[i]);
auto it = possible.lower_bound(min(a[i], b[i]));
pref.pridx_a =
lower_bound(compressor_a.begin(), compressor_a.end(), *it) -
compressor_a.begin();
pref.pridx_b =
lower_bound(compressor_b.begin(), compressor_b.end(), *it) -
compressor_b.begin();
suff.pridx_a =
lower_bound(compressor_a.begin(), compressor_a.end(), *it + 1) -
compressor_a.begin();
suff.pridx_b =
lower_bound(compressor_b.begin(), compressor_b.end(), *it + 1) -
compressor_b.begin();
while (it != possible.end()) {
int p = *it;
int cpap = pref.cpa(p);
int cpbp = pref.cpb(p);
int cpapp = pref.cpa(p + 1);
int cpbpp = pref.cpb(p + 1);
int alpha = pref.FTmx[cpbp];
int beta = pref.FTmx[cpbpp] - pref.FTmx[cpbp];
int gamma = pref.FTmn[cpapp] - pref.FTmn[cpap];
int delta = pref.sz - pref.FTmn[cpapp];
int epsilon = pref.sz - alpha - beta - gamma - delta;
// Case left = p
int mem_left =
delta == 0
? 1ll * pow2[alpha] *
fastmod(pow2[beta] + (gamma == 0 ? MOD - 1 : 0)) % MOD
: 0;
cpap = suff.cpa(p + 1);
cpbp = suff.cpb(p + 1);
cpapp = suff.cpa(p + 2);
cpbpp = suff.cpb(p + 2);
int alpha_ = suff.FTmx[cpbp];
int beta_ = suff.FTmx[cpbpp] - suff.FTmx[cpbp];
int gamma_ = suff.FTmn[cpapp] - suff.FTmn[cpap];
int delta_ = suff.sz - suff.FTmn[cpapp];
int epsilon_ = suff.sz - alpha_ - beta_ - gamma_ - delta_;
int g =
gamma_ + delta_ != 0
? pow2[suff.sz]
: fastmod((epsilon_ != 0
? 1ll * fastmod(pow2[epsilon_] + MOD - 1) *
pow2[alpha_ + beta_] % MOD
: 0) +
1ll * pow2[alpha_] *
fastmod(pow2[beta_] + MOD - 1) % MOD);
if (p > a[i]) {
ans += 1ll * mem_left * g % MOD * (p - a[i]) % MOD;
ans = fastmod(ans);
if (p > b[i]) {
ans += 1ll * mem_left * g % MOD * (p - b[i]) % MOD;
ans = fastmod(ans);
}
}
it++;
}
pref.insert(a[i], b[i]);
}
return ans;
}
int solve_geq(int n) {
int ans = 0;
QueryMaintainer pref, suff;
map<int, int> possible;
for (int i = 0; i < n; i++) {
suff.insert(a[i], b[i]);
possible[a[i]]++;
possible[b[i]]++;
}
for (int i = 0; i < n; i++) {
possible[a[i]]--;
possible[b[i]]--;
if (possible[a[i]] == 0)
possible.erase(a[i]);
if (possible[b[i]] == 0)
possible.erase(b[i]);
suff.erase(a[i], b[i]);
auto it = possible.lower_bound(min(a[i], b[i]));
pref.pridx_a =
lower_bound(compressor_a.begin(), compressor_a.end(), it->first) -
compressor_a.begin();
pref.pridx_b =
lower_bound(compressor_b.begin(), compressor_b.end(), it->first) -
compressor_b.begin();
suff.pridx_a =
lower_bound(compressor_a.begin(), compressor_a.end(), it->first) -
compressor_a.begin();
suff.pridx_b =
lower_bound(compressor_b.begin(), compressor_b.end(), it->first) -
compressor_b.begin();
while (it != possible.end()) {
int q = it->first;
int cpap = pref.cpa(q);
int cpbp = pref.cpb(q);
int cpapp = pref.cpa(q + 1);
int cpbpp = pref.cpb(q + 1);
int alpha = pref.FTmx[cpbp];
int beta = pref.FTmx[cpbpp] - pref.FTmx[cpbp];
int gamma = pref.FTmn[cpapp] - pref.FTmn[cpap];
int delta = pref.sz - pref.FTmn[cpapp];
int epsilon = pref.sz - alpha - beta - gamma - delta;
// Case left >= q
int mem_left =
gamma + delta != 0
? pow2[pref.sz]
: fastmod((epsilon != 0
? 1ll * fastmod(pow2[epsilon] + MOD - 1) *
pow2[alpha + beta] % MOD
: 0) +
1ll * pow2[alpha] *
fastmod(pow2[beta] + MOD - 1) % MOD);
cpap = suff.cpa(q);
cpbp = suff.cpb(q);
cpapp = suff.cpa(q + 1);
cpbpp = suff.cpb(q + 1);
int alpha_ = suff.FTmx[cpbp];
int beta_ = suff.FTmx[cpbpp] - suff.FTmx[cpbp];
int gamma_ = suff.FTmn[cpapp] - suff.FTmn[cpap];
int delta_ = suff.sz - suff.FTmn[cpapp];
int epsilon_ = suff.sz - alpha_ - beta_ - gamma_ - delta_;
// Case left >= q, right = q
int e =
delta_ == 0
? 1ll * pow2[alpha_] *
fastmod(pow2[beta_] + (gamma_ == 0 ? MOD - 1 : 0)) %
MOD
: 0;
if (q > a[i]) {
ans += 1ll * mem_left * e % MOD * (q - a[i]) % MOD;
ans = fastmod(ans);
if (q > b[i]) {
ans += 1ll * mem_left * e % MOD * (q - b[i]) % MOD;
ans = fastmod(ans);
}
}
it++;
}
pref.insert(a[i], b[i]);
}
return ans;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n;
cin >> n;
pow2[0] = 1;
for (int i = 1; i <= n; i++)
pow2[i] = 2 * pow2[i - 1] % MOD;
for (int i = 0; i < n; i++) {
cin >> a[i];
}
for (int i = 0; i < n; i++) {
cin >> b[i];
if (a[i] > b[i])
swap(a[i], b[i]);
compressor_a.push_back(a[i]);
compressor_b.push_back(b[i]);
}
sort(compressor_a.begin(), compressor_a.end());
compressor_a.resize(unique(compressor_a.begin(), compressor_a.end()) -
compressor_a.begin());
sort(compressor_b.begin(), compressor_b.end());
compressor_b.resize(unique(compressor_b.begin(), compressor_b.end()) -
compressor_b.begin());
cout << fastmod(solve_exact(n) + solve_geq(n)) << endl;
return 0;
}
