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| #include <bits/stdc++.h>
using namespace std;
#define lson(u) node[u].l
#define rson(u) node[u].r
#define ge(x) (lower_bound(a + 1, a + N + 1, x) - a)
#define le(x) (upper_bound(a + 1, a + N + 1, x) - a - 1)
typedef long long ll;
const int maxn = 1000005;
const int mod = 1000000007;
const int inf = 0x3f3f3f3f;
struct Node {
int l, r;
}node[maxn << 1];
int cnt;
int N, R, ans;
ll a[maxn], r[maxn];
int num[maxn], range[maxn][2];
vector<int> G[maxn], SCC[maxn];
int w[maxn], dfn[maxn], low[maxn], dfn_idx;
int scc[maxn], scc_cnt;
bool ins[maxn];
stack<int> s;
int f[maxn][2];
bool vis[maxn];
void build(int& u, int l, int r) {
u = ++cnt;
range[u][0] = l, range[u][1] = r;
if (l == r) {
num[l] = u;
w[u] = 1;
return;
}
int mid = (l + r) >> 1;
build(lson(u), l, mid), build(rson(u), mid + 1, r);
G[u].push_back(lson(u)), G[u].push_back(rson(u));
}
void add_edge_range(int u, int l, int r, int qu, int ql, int qr) {
if (ql <= l && r <= qr) {
G[qu].push_back(u);
return;
}
int mid = (l + r) >> 1;
if (ql <= mid) add_edge_range(lson(u), l, mid, qu, ql, qr);
if (mid < qr) add_edge_range(rson(u), mid + 1, r, qu, ql, qr);
}
void tarjan(int u) {
low[u] = dfn[u] = ++dfn_idx;
ins[u] = 1;
s.push(u);
for (vector<int>::iterator it = G[u].begin(); it != G[u].end(); it++) {
int v = *it;
if (dfn[v] == 0) {
tarjan(v);
low[u] = min(low[u], low[v]);
} else if (ins[v]) {
low[u] = min(low[u], dfn[v]);
}
}
if (low[u] == dfn[u]) {
scc_cnt++;
f[scc_cnt][0] = inf, f[scc_cnt][1] = -inf;
while (ins[u]) {
int t = s.top();
s.pop();
ins[t] = 0;
scc[t] = scc_cnt;
f[scc_cnt][0] = min(f[scc_cnt][0], range[t][0]);
f[scc_cnt][1] = max(f[scc_cnt][1], range[t][1]);
}
}
}
void dp(int u) {
if (vis[u]) return;
vis[u] = 1;
for (vector<int>::iterator it = SCC[u].begin(); it != SCC[u].end(); it++) {
int v = *it;
dp(v);
f[u][0] = min(f[u][0], f[v][0]);
f[u][1] = max(f[u][1], f[v][1]);
}
}
int main() {
scanf("%d", &N);
for (int i = 1; i <= N; ++i)
scanf("%lld%lld", &a[i], &r[i]);
build(R, 1, N);
for (int i = 1; i <= N; ++i)
add_edge_range(R, 1, N, num[i], ge(a[i] - r[i]), le(a[i] + r[i]));
tarjan(1);
for (int u = 1; u <= N; ++u) {
for (vector<int>::iterator it = G[u].begin(); it != G[u].end(); it++) {
int v = *it;
if (scc[u] != scc[v])
SCC[scc[u]].push_back(scc[v]);
}
}
for (int i = 1; i <= scc_cnt; ++i)
dp(i);
for (int i = 1; i <= N; ++i) {
ans = (ans + 1ll * i * (f[scc[num[i]]][1] - f[scc[num[i]]][0] + 1)) % mod;
}
printf("%d", ans);
return 0;
}
|