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#include <memory>
#include <vector>
template <typename Node, typename Impl> struct SegmentTreeBase {
explicit SegmentTreeBase(int n_) : n(n_), nodes(n << 1) {}
Node &root() { return get_node(0, n - 1); }
const Node &root() const { return get_node(0, n - 1); }
template <typename H> H traverse_all(H &&h) {
traverse_all(std::forward<H>(h), 0, n - 1);
return h;
}
template <typename H> H traverse(H &&h, int a, int b) {
traverse<H, 0>(std::forward<H>(h), 0, n - 1, a, b);
return h;
}
template <typename H> H reverse_traverse(H &&h, int a, int b) {
traverse<H, 1>(std::forward<H>(h), 0, n - 1, a, b);
return h;
}
Node &get_node(int l, int r) { return nodes[l + r | (l != r)]; }
protected:
template <typename Op> void traverse_all(Op &&op, int l, int r) {
Node &n = get_node(l, r);
op(l, r, n);
if (l < r) {
int m = (l + r) >> 1;
Node &ln = get_node(l, m);
Node &rn = get_node(m + 1, r);
static_cast<Impl *>(this)->propagate(l, m, r, n, ln, rn);
traverse_all(std::forward<Op>(op), l, m);
traverse_all(std::forward<Op>(op), m + 1, r);
static_cast<Impl *>(this)->collect(l, m, r, n, ln, rn);
}
}
template <typename Op, int direction>
void traverse(Op &&op, int l, int r, int a, int b) {
if (b < l || r < a) {
return;
}
Node &n = get_node(l, r);
if (a <= l && r <= b) {
op(l, r, n);
} else {
int m = (l + r) >> 1;
Node &ln = get_node(l, m);
Node &rn = get_node(m + 1, r);
static_cast<Impl *>(this)->propagate(l, m, r, n, ln, rn);
if (direction) {
traverse<Op, 1>(std::forward<Op>(op), m + 1, r, a, b);
traverse<Op, 1>(std::forward<Op>(op), l, m, a, b);
} else {
traverse<Op, 0>(std::forward<Op>(op), l, m, a, b);
traverse<Op, 0>(std::forward<Op>(op), m + 1, r, a, b);
}
static_cast<Impl *>(this)->collect(l, m, r, n, ln, rn);
}
}
int n;
std::vector<Node> nodes;
};
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