#include <bits/stdc++.h>
#define FOR(i,a,b) for(int i= (a); i<((int)b); ++i)
#define RFOR(i,a) for(int i=(a); i >= 0; --i)
#define FOE(i,a) for(auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define DUMP(x) cerr << #x << " = " << (x) << endl;
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v,x) (std::find(v.begin(), v.end(), x) != v.end())
#define BIT_ON(bit, i) (bit & (1LL << i))
typedef long long LL;
template<typename T> using V = std::vector<T>;
template<typename T> using VV = std::vector<std::vector<T>>;
template<typename T> using VVV = std::vector<std::vector<std::vector<T>>>;
template<typename T> using VVVV = std::vector<std::vector<std::vector<std::vector<T>>>>;
template<class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }
template<class T> inline void print(T x) { std::cout << x << std::endl; }
template<class T> inline void print_vec(const std::vector<T> &v) { for (int i = 0; i < v.size(); ++i) { if (i != 0) {std::cout << " ";} std::cout << v[i];} std::cout << "\n"; }
template<class T> inline bool inside(T y, T x, T H, T W) {return 0 <= y and y < H and 0 <= x and x < W; }
template<class T> inline double euclidean_distance(T y1, T x1, T y2, T x2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); }
template<class T> inline double manhattan_distance(T y1, T x1, T y2, T x2) { return abs(x1 - x2) + abs(y1 - y2); }
template<typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }
template<class T> inline std::vector<T> unique(std::vector<T> v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
return v;
}
// 初項s, 交差dのn個の数列の和
long long sum_of_arithmetic_progression(long long s, long long d, long long n) {
return n * (2 * s + (n - 1) * d) / 2;
}
const int INF = 1 << 30;
const double EPS = 1e-9;
const std::string YES = "YES", Yes = "Yes", NO = "NO", No = "No";
const std::vector<int> dy4 = {0, -1, 0, 1}, dx4 = {1, 0, -1, 0};
const std::vector<int> dy8 = { 0, -1, 0, 1, 1, -1, -1, 1 }, dx8 = { 1, 0, -1, 0, 1, 1, -1, -1 };
#include<bits/stdc++.h>
//#define USE_GRAPHVIZ
#ifdef USE_GRAPHVIZ
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graphviz.hpp>
#endif
enum {
NOTFOUND = 0xFFFFFFFFFFFFFFFFLLU
};
uint64_t NODE_NO = 0;
class Node {
public:
uint64_t no; // node番号
// internal nodeのときに使用
uint64_t num; // 左の子の部分木のもつbitの数
uint64_t ones; // 左の子の部分木のもつ1の数
Node *left;
Node *right;
int64_t balance; // 右の子の高さ - 左の子の高さ.+なら右の子の方が高い,-なら左の子の方が高い
// leafのときに使用
uint64_t bits; // bit
uint64_t bits_size; // bitのサイズ(debug用)
bool is_leaf;
Node(uint64_t bits, uint64_t bits_size, bool is_leaf) : no(NODE_NO++), num(0), ones(0), bits(bits), bits_size(bits_size), is_leaf(is_leaf), left(nullptr), right(nullptr), balance(0) {}
bool is_valid_node() {
if (is_leaf) {
if (num != 0) { return false; }
if (ones != 0) { return false; }
if (left != nullptr) { return false; }
if (right != nullptr) { return false; }
}
else {
if (num == 0) { return false; }
if (left == nullptr) { return false; }
if (right == nullptr) { return false; }
if (bits != 0) { return false; }
if (bits_size != 0) { return false; }
if (ones > num) {return false; }
}
return true;
}
std::string info() {
std::string str = "No:" + std::to_string(this->no) + "\n";
if (is_leaf) {
str += "size:" + std::to_string(this->bits_size) + "\n";
for (int i = 0; i < bits_size; ++i) {
str += std::to_string((bits >> (uint64_t)i) & (uint64_t)1);
}
}
else {
str += "num:" + std::to_string(this->num) + " ones:" + std::to_string(this->ones) + "\n";
}
return str;
}
};
class DynamicBitVector {
public:
Node *root;
uint64_t size; // 全体のbitの数
uint64_t num_one; // 全体の1の数
const uint64_t bits_size_limit = 32; // 各ノードが管理するbitの長さ制限.2 * bits_size_limit以上になったらノードを分割し, 1/2*bits_size_limit以下になったらノードを結合する
DynamicBitVector(): root(nullptr), size(0), num_one(0) {}
DynamicBitVector(std::vector<uint64_t> &v): root(nullptr), size(0), num_one(0) {
if (v.size() == 0) {
return;
}
std::deque<std::pair<Node*, uint64_t>> leaves;
for (int i = 0; i < v.size(); i += this->bits_size_limit) {
uint64_t bits = 0;
const uint64_t bits_size = std::min(this->bits_size_limit, (uint64_t)v.size() - i);
for (int j = 0; j < bits_size; ++j) {
assert(v[i + j] == 0 or v[i + j] == 1);
if (v[i + j] == 1) {
bits |= (uint64_t)1 << j;
}
}
leaves.emplace_back(std::make_pair(new Node(bits, bits_size, true), bits_size));
}
std::deque<std::tuple<Node*, uint64_t, uint64_t, uint64_t>> nodes; // (node, 全体のbit数, 全体の1の数, 高さ)
while (not leaves.empty()) {
const auto node = leaves.front().first;
const auto bits_size = leaves.front().second;
leaves.pop_front();
nodes.emplace_back(std::make_tuple(node, bits_size, popCount(node->bits), 0));
}
while (nodes.size() > 1) {
std::deque<std::tuple<Node*, uint64_t, uint64_t, uint64_t>> next_nodes;
while (not nodes.empty()) {
// あまりがでたときは,最後に作った中間ノードと結合させるためにnodesに戻す
if (nodes.size() == 1) {
nodes.push_front(next_nodes.back());
next_nodes.pop_back();
}
Node *left_node;
uint64_t left_num, left_ones, left_height;
std::tie(left_node, left_num, left_ones, left_height) = nodes.front(); nodes.pop_front();
Node *right_node;
uint64_t right_num, right_ones, right_height;
std::tie(right_node, right_num, right_ones, right_height) = nodes.front(); nodes.pop_front();
const auto internal_node = new Node(0, 0, false);
internal_node->num = left_num;
internal_node->ones = left_ones;
internal_node->left = left_node;
internal_node->right = right_node;
internal_node->balance = right_height - left_height;
next_nodes.emplace_back(std::make_tuple(internal_node, left_num + right_num, left_ones + right_ones, std::max(left_height, right_height) + 1));
}
nodes = next_nodes;
}
uint64_t height;
std::tie(this->root, this->size, this->num_one, height) = nodes.front(); nodes.pop_front();
assert(this->size == v.size());
}
// B[pos]
uint64_t access(uint64_t pos) {
assert(pos < this->size);
return access(this->root, pos);
}
// B[0, pos)にある指定されたbitの数
uint64_t rank(uint64_t bit, uint64_t pos) {
assert(bit == 0 or bit == 1);
assert(pos <= this->size);
if (bit) {
return rank1(this->root, pos, 0);
}
else {
return pos - rank1(this->root, pos, 0);
}
}
// rank番目の指定されたbitの位置 + 1(rankは1-origin)
uint64_t select(uint64_t bit, uint64_t rank) {
assert(bit == 0 or bit == 1);
assert(rank > 0);
if (bit == 0 and rank > this->size - this-> num_one) { return NOTFOUND; }
if (bit == 1 and rank > this-> num_one) { return NOTFOUND; }
if (bit) {
return select1(this->root, 0, rank);
}
else {
return select0(this->root, 0, rank);
}
}
// posにbitを挿入する
void insert(uint64_t pos, uint64_t bit) {
assert(bit == 0 or bit == 1);
assert(pos <= this->size); // 現在もってるbitsの末尾には挿入できる
if (root == nullptr) {
root = new Node(bit, 1, true);
} else {
insert(this->root, nullptr, bit, pos, this->size);
}
this->size++;
this->num_one += (bit == 1);
}
// 末尾にbitを追加する
void push_back(uint64_t bit) {
assert(bit == 0 or bit == 1);
this->insert(this->size, bit);
}
// posを削除する
void erase(uint64_t pos) {
assert(pos < this->size);
uint64_t bit = this->remove(this->root, nullptr, pos, this->size, 0, true).first;
this->size--;
this->num_one -= (bit == 1);
}
// posにbitをセットする
void update(uint64_t pos, uint64_t bit) {
assert(bit == 0 or bit == 1);
assert(pos < this->size);
if (bit == 1) {
this->bitset(pos);
}
else {
this->bitclear(pos);
}
}
// posのbitを1にする
void bitset(uint64_t pos) {
assert(pos < this->size);
bool flip = bitset(this->root, pos);
this->num_one += flip;
}
// posのbitを0にする
void bitclear(uint64_t pos) {
assert(pos < this->size);
bool flip = bitclear(this->root, pos);
this->num_one -= flip;
}
// dotファイルを作成する(debug用)
void graphviz(const std::string &file_path) {
#ifdef USE_GRAPHVIZ
boost::adjacency_list<> graph;
std::vector<std::string> labels;
auto root = boost::add_vertex(graph);
labels.emplace_back(this->root->info());
std::queue<std::pair<Node*, boost::adjacency_list<>::vertex_descriptor>> que;
que.emplace(std::make_pair(this->root, root));
while (not que.empty()) {
Node *node = que.front().first;
auto parent = que.front().second;
que.pop();
if (not node->is_leaf) {
// left
auto left = boost::add_vertex(graph);
boost::add_edge(parent, left, graph);
labels.emplace_back("L\n" + node->left->info());
que.emplace(std::make_pair(node->left, left));
// right
auto right = boost::add_vertex(graph);
boost::add_edge(parent, right, graph);
labels.emplace_back("R\n" + node->right->info());
que.emplace(std::make_pair(node->right, right));
}
}
std::ofstream file(file_path);
boost::write_graphviz(file, graph, boost::make_label_writer(&labels[0]));
#else
std::cerr << "please define USE_GRAPHVIZ" << std::endl;
#endif
}
// 木の状態が正しいかチェックする(debug用)
// 各ノードのbalanceの値が正しいか.AVL木の制約を守っているかのチェック
bool is_valid_tree(bool verbose) {
if (this->root == nullptr) {
if (this->size == 0 and this->num_one == 0) {
return true;
}
std::cerr << "root is nullptr but size is " << this->size << " and num_one is " << this->num_one << std::endl;
return false;
}
std::map<uint64_t, uint64_t> height;
get_height(this->root, height);
std::queue<Node*> que;
que.emplace(this->root);
while (not que.empty()) {
Node *node = que.front(); que.pop();
if (not node->is_valid_node()) {
if (verbose) {
std::cerr << "node " << node->no << " is invalid node" << std::endl;
std::cerr << node->info() << std::endl;
}
return false;
}
if (not node->is_leaf) {
auto left_height = height[node->left->no];
auto right_height = height[node->right->no];
// バランスの値が正しいかチェック
if (node->balance != right_height - left_height) {
if (verbose) {
std::cerr << "node" << node->no << "'s balance is " << node->balance << "(left height:" << left_height << ", right height:" << right_height << ")" << std::endl;
}
return false;
}
// AVL木の制約を満たしていない
if (node->balance < -1 or 1 < node->balance) {
if (verbose) {
std::cerr << "node" << node->no << "is not balanced." << "(balance:" << node->balance << ", left height:" << left_height << ", right height:" << right_height << ")" << std::endl;
}
return false;
}
que.emplace(node->left);
que.emplace(node->right);
}
else {
// バランスの値が正しいかチェック
if (node->balance != 0) {
if (verbose) {
std::cerr << "node " << node->no << "'s balance is not 0" << std::endl;
}
return false;
}
}
}
return true;
}
private:
uint64_t access(const Node *node, uint64_t pos) {
if (node->is_leaf) {
assert(pos <= 2 * this->bits_size_limit);
return (node->bits >> pos) & (uint64_t)1;
}
if (pos < node->num) {
return this->access(node->left, pos);
} else {
return this->access(node->right, pos - node->num);
}
}
uint64_t rank1(const Node *node, uint64_t pos, uint64_t ones) {
if (node->is_leaf) {
assert(node->bits_size >= pos);
const uint64_t mask = ((uint64_t)1 << pos) - 1;
return ones + popCount(node->bits & mask);
}
if (pos < node->num) {
return this->rank1(node->left, pos, ones);
} else {
return this->rank1(node->right, pos - node->num, ones + node->ones);
}
}
uint64_t select1(const Node *node, uint64_t pos, uint64_t rank) {
if (node->is_leaf) {
return pos + this->selectInBlock(node->bits, rank) + 1;
}
if (rank <= node->ones) {
return this->select1(node->left, pos, rank);
} else {
return this->select1(node->right, pos + node->num, rank - node->ones);
}
}
uint64_t select0(const Node *node, uint64_t pos, uint64_t rank) {
if (node->is_leaf) {
return pos + this->selectInBlock(~node->bits, rank) + 1;
}
if (rank <= (node->num - node->ones)) {
return this->select0(node->left, pos, rank);
} else {
return this->select0(node->right, pos + node->num, rank - (node->num - node->ones));
}
}
// bits(64bit)のrank番目(0-index)の1の数
uint64_t selectInBlock(uint64_t bits, uint64_t rank) {
const uint64_t x1 = bits - ((bits & 0xAAAAAAAAAAAAAAAALLU) >> (uint64_t)1);
const uint64_t x2 = (x1 & 0x3333333333333333LLU) + ((x1 >> (uint64_t)2) & 0x3333333333333333LLU);
const uint64_t x3 = (x2 + (x2 >> (uint64_t)4)) & 0x0F0F0F0F0F0F0F0FLLU;
uint64_t pos = 0;
for (;; pos += 8){
const uint64_t rank_next = (x3 >> pos) & 0xFFLLU;
if (rank <= rank_next) break;
rank -= rank_next;
}
const uint64_t v2 = (x2 >> pos) & 0xFLLU;
if (rank > v2) {
rank -= v2;
pos += 4;
}
const uint64_t v1 = (x1 >> pos) & 0x3LLU;
if (rank > v1){
rank -= v1;
pos += 2;
}
const uint64_t v0 = (bits >> pos) & 0x1LLU;
if (v0 < rank){
pos += 1;
}
return pos;
}
// nodeから辿れる葉のpos番目にbitをいれる(葉のbitの長さはlen)
// 高さの変化を返す
int64_t insert(Node *node, Node *parent, uint64_t bit, uint64_t pos, uint64_t len) {
assert(bit == 0 or bit == 1);
if (node->is_leaf) {
assert(pos <= 2 * this->bits_size_limit);
// posより左をとりだす
const uint64_t up_mask = (((uint64_t)1 << (len - pos)) - 1) << pos;
const uint64_t up = (node->bits & up_mask);
// posより右をとりだす
const uint64_t down_mask = ((uint64_t)1 << pos) - 1;
const uint64_t down = node->bits & down_mask;
node->bits = (up << (uint64_t)1) | (bit << pos) | down;
node->bits_size++;
assert(node->bits_size == len + 1);
// bitsのサイズが大きくなったので分割する
if (len + 1 >= 2 * bits_size_limit) {
this->splitNode(node, len + 1); // 引数のlenはinsert後の長さなので+1する
return 1;
}
return 0;
}
if (pos < node->num) {
const int64_t diff = this->insert(node->left, node, bit, pos, node->num);
node->num += 1;
node->ones += (bit == 1);
return achieveBalance(parent, node, diff, 0);
} else {
const int64_t diff = this->insert(node->right, node, bit, pos - node->num, len - node->num);
return achieveBalance(parent, node, 0, diff);
}
}
// nodeのpos番目のbitを削除する
// 消したbitと高さの変化のpairを返す
std::pair<uint64_t, int64_t> remove(Node *node, Node *parent, uint64_t pos, uint64_t len, uint64_t ones, bool allow_under_flow) {
if (node->is_leaf) {
// 消すとunder flowになるので消さない
if (node != this->root and len <= bits_size_limit / 2 and not allow_under_flow) {
return std::make_pair(NOTFOUND, 0);
}
assert(pos <= 2 * this->bits_size_limit);
assert(pos < len);
const uint64_t bit = (node->bits >> pos) & (uint64_t)1;
// posより左をとりだす(posを含まないようにする)
const uint64_t up_mask = (((uint64_t)1 << (len - pos - 1)) - 1) << (pos + 1);
const uint64_t up = (node->bits & up_mask);
// posより右をとりだす
const uint64_t down_mask = ((uint64_t)1 << pos) - 1;
const uint64_t down = node->bits & down_mask;
node->bits = (up >> (uint64_t)1) | down;
node->bits_size--;
assert(node->bits_size == len - 1);
return std::make_pair(bit, 0);
}
if (pos < node->num) {
const auto bit_diff = this->remove(node->left, node, pos, node->num, node->ones, allow_under_flow);
if (bit_diff.first == NOTFOUND) {
return bit_diff;
}
node->ones -= (bit_diff.first == 1);
// 左の子の葉のbitを1つ消したのでunder flowが発生している
if (node->num == bits_size_limit / 2) {
const auto b_d = remove(node->right, node, 0, len - bits_size_limit / 2, 0, false); // 右の葉の先頭bitを削る
// 右の葉もunder flowになって消せない場合は2つの葉を統合する
if (b_d.first == NOTFOUND) {
assert(node->left->is_leaf);
assert(node->left->bits_size == bits_size_limit / 2 - 1);
// 右の子から辿れる一番左の葉の先頭にleftのbitsを追加する
mergeNodes(node->right, 0, len - bits_size_limit / 2, node->left->bits, bits_size_limit / 2 - 1, node->ones, true);
this->replace(parent, node, node->right); // parentの子のnodeをnode->rightに置き換える
return std::make_pair(bit_diff.first, -1);
}
// 右の葉からとった先頭bitを左の葉の末尾にいれる
assert(node->left->bits_size == bits_size_limit / 2 - 1);
insert(node->left, node, b_d.first, bits_size_limit / 2 - 1, bits_size_limit / 2 - 1);
node->ones += (b_d.first == 1);
}
else {
node->num -= 1;
}
const int64_t diff = achieveBalance(parent, node, bit_diff.second, 0);
return std::make_pair(bit_diff.first, diff);
} else {
const auto bit_diff = this->remove(node->right, node, pos - node->num, len - node->num, ones - node->ones, allow_under_flow);
if (bit_diff.first == NOTFOUND) {
return bit_diff;
}
ones -= (bit_diff.first == 1);
// 右の子の葉のbitを1つ消したのでunder flowが発生する
if ((len - node->num) == bits_size_limit / 2) {
const auto b_d = remove(node->left, node, node->num - 1, node->num, 0, false); // 左の葉の末尾をbitを削る
// 左の葉もunder flowになって消せない場合は2つの葉を統合する
if (b_d.first == NOTFOUND) {
assert(node->right->is_leaf);
assert(node->right->bits_size == bits_size_limit / 2 - 1);
// 左の子から辿れる一番右の葉の末尾にleftのbitsを追加する
mergeNodes(node->left, node->num, node->num, node->right->bits, bits_size_limit / 2 - 1, ones - node->ones, false);
this->replace(parent, node, node->left); // parentの子のnodeをnode->leftに置き換える
return std::make_pair(bit_diff.first, -1);
}
// 左の葉からとった最後尾bitを右の葉の先頭にいれる
insert(node->right, node, b_d.first, 0, bits_size_limit / 2 - 1);
node->num -= 1;
node->ones -= (b_d.first == 1);
}
const int64_t diff = achieveBalance(parent, node, 0, bit_diff.second);
return std::make_pair(bit_diff.first, diff);
}
}
// pos番目のbitを1にする.0から1への反転が起きたらtrueを返す
bool bitset(Node *node, uint64_t pos) {
if (node->is_leaf) {
assert(pos <= 2 * this->bits_size_limit);
const uint64_t bit = (node->bits >> pos) & 1;
if (bit == 1) {
return false;
}
node->bits |= ((uint64_t)1 << pos);
return true;
}
if (pos < node->num) {
bool flip = this->bitset(node->left, pos);
node->ones += flip;
return flip;
} else {
return this->bitset(node->right, pos - node->num);
}
}
// pos番目のbitを0にする.1から0への反転が起きたらtrueを返す
bool bitclear(Node *node, uint64_t pos) {
if (node->is_leaf) {
assert(pos <= 2 * this->bits_size_limit);
const uint64_t bit = (node->bits >> pos) & 1;
if (bit == 0) {
return false;
}
node->bits &= ~((uint64_t)1 << pos);
return true;
}
if (pos < node->num) {
const bool flip = this->bitclear(node->left, pos);
node->ones -= flip;
return flip;
} else {
return this->bitclear(node->right, pos - node->num);
}
}
// nodeを2つの葉に分割する
void splitNode(Node *node, uint64_t len) {
assert(node->is_leaf);
assert(node->bits_size == len);
// 左の葉
const uint64_t left_size = len / 2;
const uint64_t left_bits = node->bits & (((uint64_t)1 << left_size) - 1);
node->left = new Node(left_bits, left_size, true);
// 右の葉
const uint64_t right_size = len - left_size;
const uint64_t right_bits = node->bits >> left_size;
node->right = new Node(right_bits, right_size, true);
// nodeを内部ノードにする
node->is_leaf = false;
node->num = left_size;
node->ones = this->popCount(left_bits);
node->bits = 0;
node->bits_size = 0;
}
// nodeから辿れる葉のpos番目にbitsを格納する
void mergeNodes(Node *node, uint64_t pos, uint64_t len, uint64_t bits, uint64_t s, uint64_t ones, bool left) {
if (node->is_leaf) {
if (left) {
node->bits = (node->bits << s) | bits;
}
else {
assert(len == node->bits_size);
node->bits = node->bits | (bits << len);
}
node->bits_size += s;
return;
}
if (pos < node->num) {
node->num += s;
node->ones += ones;
mergeNodes(node->left, pos, node->num, bits, s, ones, left);
}
else {
mergeNodes(node->right, pos, len - node->num, bits, s, ones, left);
}
}
// nodeの左の高さがleftHeightDiffだけ変わり,右の高さがrightHeightDiffだけ変わったときにnodeを中心に回転させる
// 高さの変化を返す
int64_t achieveBalance(Node *parent, Node *node, int64_t leftHeightDiff, int64_t rightHeightDiff) {
assert(-1 <= node->balance and node->balance <= 1);
assert(-1 <= leftHeightDiff and leftHeightDiff <= 1);
assert(-1 <= rightHeightDiff and rightHeightDiff <= 1);
if (leftHeightDiff == 0 and rightHeightDiff == 0) {
return 0;
}
int64_t heightDiff = 0;
// 左が高いときに,左が高くなる or 右が高いときに右が高くなる
if ((node->balance <= 0 and leftHeightDiff > 0) or (node->balance >= 0 and rightHeightDiff > 0)) {
++heightDiff;
}
// 左が高いときに左が低くなる or 右が高いときに右が低くなる
if ((node->balance < 0 and leftHeightDiff < 0) or (node->balance > 0 and rightHeightDiff < 0)) {
--heightDiff;
}
node->balance += -leftHeightDiff + rightHeightDiff;
assert(-2 <= node->balance and node->balance <= 2);
// 左が2高い
if (node->balance == -2) {
assert(-1 <= node->left->balance and node->left->balance <= 1);
if (node->left->balance != 0) {
heightDiff--;
}
if (node->left->balance == 1) {
replace(node, node->left, rotateLeft(node->left));
}
replace(parent, node, rotateRight(node));
}
// 右が2高い
else if (node->balance == 2) {
assert(-1 <= node->right->balance and node->right->balance <= 1);
if (node->right->balance != 0) {
heightDiff--;
}
if (node->right->balance == -1) {
replace(node, node->right, rotateRight(node->right));
}
replace(parent, node, rotateLeft(node));
}
return heightDiff;
}
// node Bを中心に左回転する.新しい親を返す
Node *rotateLeft(Node *B) {
Node *D = B->right;
const int64_t heightC = 0;
const int64_t heightE = heightC + D->balance;
const int64_t heightA = std::max(heightC, heightE) + 1 - B->balance;
B->right = D->left;
D->left = B;
B->balance = heightC - heightA;
D->num += B->num;
D->ones += B->ones;
D->balance = heightE - (std::max(heightA, heightC) + 1);
assert(-2 <= B->balance and B->balance <= 2);
assert(-2 <= D->balance and D->balance <= 2);
return D;
}
// node Dを中心に右回転する.新しい親を返す
Node *rotateRight(Node *D) {
Node *B = D->left;
const int64_t heightC = 0;
const int64_t heightA = heightC - B->balance;
const int64_t heightE = std::max(heightA, heightC) + 1 + D->balance;
D->left = B->right;
B->right = D;
D->num -= B->num;
D->ones -= B->ones;
D->balance = heightE - heightC;
B->balance = std::max(heightC, heightE) + 1 - heightA;
assert(-2 <= B->balance and B->balance <= 2);
assert(-2 <= D->balance and D->balance <= 2);
return B;
}
// parentの子のoldNodeをnewNodeに置き換える
void replace(Node *parent, Node *oldNode, Node *newNode) {
if (parent == nullptr) {
this->root = newNode;
return;
}
if (parent->left == oldNode) {
parent->left = newNode;
}
else if (parent->right == oldNode) {
parent->right = newNode;
}
else {
throw "old node is not child";
}
}
uint64_t popCount(uint64_t x) {
x = (x & 0x5555555555555555ULL) + ((x >> (uint64_t)1) & 0x5555555555555555ULL);
x = (x & 0x3333333333333333ULL) + ((x >> (uint64_t)2) & 0x3333333333333333ULL);
x = (x + (x >> (uint64_t)4)) & 0x0f0f0f0f0f0f0f0fULL;
x = x + (x >> (uint64_t)8);
x = x + (x >> (uint64_t)16);
x = x + (x >> (uint64_t)32);
return x & 0x7FLLU;
}
// 各ノードの高さ(一番遠い葉からの距離)を取得(debug用)
uint64_t get_height(Node *node, std::map<uint64_t, uint64_t> &height) {
if (node->is_leaf) {
return 0;
}
if (height.find(node->no) != height.end()) {
return height[node->no];
}
auto left_height = get_height(node->left, height);
auto right_height = get_height(node->right, height);
return height[node->no] = std::max(left_height, right_height) + 1;
}
};
class DynamicWaveletMatrix {
public:
std::vector<DynamicBitVector> bit_arrays;
std::vector<uint64_t> begin_one; // 各bitの1の開始位置
uint64_t size; // 与えられた配列のサイズ
uint64_t maximum_element; // 最大の文字
uint64_t bit_size; // 文字を表すのに必要なbit数
public:
// max_element: 入ってくる中で一番大きい数値
DynamicWaveletMatrix (uint64_t maximum_element) : size(0), maximum_element(maximum_element + 1) {
this->bit_size = this->get_num_of_bit(maximum_element);
if (bit_size == 0) {
bit_size = 1;
}
this->begin_one.resize(bit_size);
for (uint64_t i = 0; i < bit_size; ++i) {
DynamicBitVector sv;
bit_arrays.push_back(sv);
}
}
DynamicWaveletMatrix (uint64_t num_of_alphabet, const std::vector<uint64_t> &array) : size(0), maximum_element(num_of_alphabet + 1) {
this->bit_size = this->get_num_of_bit(num_of_alphabet);
if (bit_size == 0) {
bit_size = 1;
}
this->begin_one.resize(bit_size);
if (array.size() == 0) {
for (uint64_t i = 0; i < bit_size; ++i) {
DynamicBitVector sv;
bit_arrays.push_back(sv);
}
return;
}
size = array.size();
std::vector<uint64_t> v(array), b(array.size(), 0);
for (uint64_t i = 0; i < bit_size; ++i) {
std::vector<uint64_t> temp;
// 0をtempにいれてく
for (uint64_t j = 0; j < v.size(); ++j) {
uint64_t c = v.at(j);
uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
if (bit == 0) {
temp.push_back(c);
b[j] = 0;
}
}
this->begin_one.at(i) = temp.size();
// 1をtempにいれてく
for (uint64_t j = 0; j < v.size(); ++j) {
uint64_t c = v.at(j);
uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
if (bit == 1) {
temp.push_back(c);
b[j] = 1;
}
}
DynamicBitVector dbv(b);
bit_arrays.emplace_back(dbv);
v = temp;
}
}
// v[pos]
uint64_t access(uint64_t pos) {
if (pos >= this->size) { return NOTFOUND; }
uint64_t c = 0;
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
uint64_t bit = bit_arrays.at(i).access(pos); // もとの数値がのi番目のbit
c = (c <<= 1) | bit;
pos = bit_arrays.at(i).rank(bit, pos);
if (bit) {
pos += this->begin_one.at(i);
}
}
return c;
}
// v[0, pos)のcの数
uint64_t rank(uint64_t c, uint64_t pos) {
assert(pos <= size);
if (c >= maximum_element) {
return 0;
}
uint64_t left = 0, right = pos;
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
left = bit_arrays.at(i).rank(bit, left); // cのi番目のbitと同じ数値の数
right = bit_arrays.at(i).rank(bit, right); // cのi番目のbitと同じ数値の数
if (bit) {
left += this->begin_one.at(i);
right += this->begin_one.at(i);
}
}
return right - left;
}
// i番目のcの位置 + 1を返す。rankは1-origin
uint64_t select(uint64_t c, uint64_t rank) {
assert(rank > 0);
if (c >= maximum_element) {
return NOTFOUND;
}
uint64_t left = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
left = bit_arrays.at(i).rank(bit, left); // cのi番目のbitと同じ数値の数
if (bit) {
left += this->begin_one.at(i);
}
}
uint64_t index = left + rank;
for (uint64_t i = 0; i < bit_arrays.size(); ++i){
uint64_t bit = ((c >> i) & 1); // 下からi番目のbit
if (bit == 1) {
index -= this->begin_one.at(bit_size - i - 1);
}
index = this->bit_arrays.at(bit_size - i - 1).select(bit, index);
}
return index;
}
// posにcを挿入する
void insert(uint64_t pos, uint64_t c) {
assert(pos <= this->size);
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
const uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
bit_arrays.at(i).insert(pos, bit);
pos = bit_arrays.at(i).rank(bit, pos);
if (bit) {
pos += this->begin_one.at(i);
}
else {
this->begin_one.at(i)++;
}
}
this->size++;
}
// 末尾にcを追加する
void push_back(uint64_t c) {
this->insert(this->size, c);
}
// posを削除する
void erase(uint64_t pos) {
assert(pos < this->size);
if (pos >= this->size) {
throw "Segmentation fault";
}
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
uint64_t bit = bit_arrays.at(i).access(pos); // もとの数値のi番目のbit
auto next_pos = bit_arrays.at(i).rank(bit, pos);
bit_arrays.at(i).erase(pos);
if (bit) {
next_pos += this->begin_one.at(i);
}
else {
this->begin_one.at(i)--;
}
pos = next_pos;
}
this->size--;
}
// posにcをセットする
void update(uint64_t pos, uint64_t c) {
assert(pos < this->size);
this->erase(pos);
this->insert(pos, c);
}
// v[begin_pos, end_pos)で最大値のindexを返す
uint64_t maxRange(uint64_t begin_pos, uint64_t end_pos) {
return quantileRange(begin_pos, end_pos, end_pos - begin_pos - 1);
}
// v[begin_pos, end_pos)で最小値のindexを返す
uint64_t minRange(uint64_t begin_pos, uint64_t end_pos) {
return quantileRange(begin_pos, end_pos, 0);
}
// v[begin_pos, end_pos)でk番目に小さい数値のindexを返す(kは0-origin)
// つまり小さい順に並べてk番目の値
uint64_t quantileRange(uint64_t begin_pos, uint64_t end_pos, uint64_t k) {
if ((end_pos > size || begin_pos >= end_pos) || (k >= end_pos - begin_pos)) {
return NOTFOUND;
}
uint64_t val = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
uint64_t num_of_zero_begin = bit_arrays.at(i).rank(0, begin_pos);
uint64_t num_of_zero_end = bit_arrays.at(i).rank(0, end_pos);
uint64_t num_of_zero = num_of_zero_end - num_of_zero_begin; // beginからendまでにある0の数
uint64_t bit = (k < num_of_zero) ? 0 : 1; // k番目の値の上からi番目のbitが0か1か
if (bit) {
k -= num_of_zero;
begin_pos = this->begin_one.at(i) + begin_pos - num_of_zero_begin;
end_pos = this->begin_one.at(i) + end_pos - num_of_zero_end;
}
else {
begin_pos = num_of_zero_begin;
end_pos = num_of_zero_begin + num_of_zero;
}
val = ((val << 1) | bit);
}
uint64_t left = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t bit = (val >> (bit_size - i - 1)) & 1; // 上からi番目のbit
left = bit_arrays.at(i).rank(bit, left); // cのi番目のbitと同じ数値の数
if (bit) {
left += this->begin_one.at(i);
}
}
uint64_t rank = begin_pos + k - left + 1;
return select(val, rank) - 1;
}
// v[0, pos)でcより小さい文字の数
uint64_t rankLessThan(uint64_t c, uint64_t pos) {
uint64_t rank_less_than = 0, rank_more_than = 0, rank = 0;
rankAll(c, 0, pos, rank, rank_less_than, rank_more_than);
return rank_less_than;
}
// v[0, pos)でcより大きい文字の数
uint64_t rankMoreThan(uint64_t c, uint64_t pos) {
uint64_t rank_less_than = 0, rank_more_than = 0, rank = 0;
rankAll(c, 0, pos, rank, rank_less_than, rank_more_than);
return rank_more_than;
}
// v[begin_pos, end_pos)でcと同じ値の数、cより小さい値の数、cより大きい値の数を求める
void rankAll(uint64_t c, uint64_t begin_pos, uint64_t end_pos, uint64_t &rank, uint64_t &rank_less_than, uint64_t &rank_more_than) {
if (c >= maximum_element || begin_pos >= size || end_pos > size) {
rank_less_than = NOTFOUND;
rank_more_than = NOTFOUND;
rank = NOTFOUND;
return;
}
rank_less_than = 0;
rank_more_than = 0;
rank = 0;
if (begin_pos >= end_pos) {
return;
}
std::vector<uint64_t> more_and_less(2, 0);
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t bit = (c >> (bit_size - i - 1)) & 1;
const uint64_t range_bits = end_pos - begin_pos;
const uint64_t begin_zero = bit_arrays.at(i).rank(0, begin_pos);
const uint64_t end_zero = bit_arrays.at(i).rank(0, end_pos);
if (bit) {
begin_pos += this->begin_one.at(i) - begin_zero;
end_pos += this->begin_one.at(i) - end_zero;
} else {
begin_pos = begin_zero;
end_pos = end_zero;
}
more_and_less.at(bit) += range_bits - (end_pos - begin_pos);
}
rank_less_than = more_and_less.at(1);
rank_more_than = more_and_less.at(0);
rank = end_pos - begin_pos;
}
// T[s1, e1)で出現回数が多い順にk個の値を返す
std::vector<std::pair<uint64_t, uint64_t>> topk(uint64_t s, uint64_t e, uint64_t k) {
assert(s < e);
std::vector<std::pair<uint64_t, uint64_t>> result;
auto c = [](const std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &l, const std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &r) {
// width
if (std::get<0>(l) != std::get<0>(r)) {
return std::get<0>(l) < std::get<0>(r);
}
// depth
if (std::get<3>(l) != std::get<3>(r)) {
return std::get<3>(l) > std::get<3>(r);
}
// value
if (std::get<4>(l) != std::get<4>(r)) {
return std::get<4>(l) > std::get<4>(r);
}
return true;
};
std::priority_queue<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>, std::vector<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>>, decltype(c)> que(c); // width, left, right, depth, value
que.push(std::make_tuple(e - s, s, e, 0, 0));
while (not que.empty()) {
auto element = que.top(); que.pop();
uint64_t width, left, right, depth, value;
std::tie(width, left, right, depth, value) = element;
if (depth >= this->bit_size) {
result.emplace_back(std::make_pair(value, right - left));
if (result.size() >= k) {
break;
}
continue;
}
// 0
const uint64_t left0 = this->bit_arrays.at(depth).rank(0, left);
const uint64_t right0 = this->bit_arrays.at(depth).rank(0, right);
if (left0 < right0) {
que.push(std::make_tuple(right0 - left0, left0, right0, depth + 1, value));
}
// 1
const uint64_t left1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, left);
const uint64_t right1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, right);
if (left1 < right1) {
que.push(std::make_tuple(right1 - left1, left1, right1, depth + 1, value | (1 << bit_size - depth - 1)));
}
}
return result;
};
// T[s1, e1)とT[s2, e2)に共通して出現する要素を求める
std::vector<std::tuple<uint64_t, uint64_t, uint64_t>> intersect(uint64_t _s1, uint64_t _e1, uint64_t _s2, uint64_t _e2) {
assert(_s1 < _e1);
assert(_s2 < _e2);
std::vector<std::tuple<uint64_t, uint64_t, uint64_t>> intersection;
std::queue<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>> que; // s1, e1, s2, e2, depth, value
que.push(std::make_tuple(_s1, _e1, _s2, _e2, 0, 0));
while (not que.empty()) {
auto e = que.front(); que.pop();
uint64_t s1, e1, s2, e2, depth, value;
std::tie(s1, e1, s2, e2, depth, value) = e;
if (depth >= this->bit_size) {
intersection.emplace_back(std::make_tuple(value, e1 - s1, e2 - s2));
continue;
}
// 0
uint64_t s1_0 = this->bit_arrays.at(depth).rank(0, s1);
uint64_t e1_0 = this->bit_arrays.at(depth).rank(0, e1);
uint64_t s2_0 = this->bit_arrays.at(depth).rank(0, s2);
uint64_t e2_0 = this->bit_arrays.at(depth).rank(0, e2);
if (s1_0 != e1_0 and s2_0 != e2_0) {
que.push(std::make_tuple(s1_0, e1_0, s2_0, e2_0, depth + 1, value));
}
// 1
uint64_t s1_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, s1);
uint64_t e1_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, e1);
uint64_t s2_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, s2);
uint64_t e2_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, e2);
if (s1_1 != e1_1 and s2_1 != e2_1) {
que.push(std::make_tuple(s1_1, e1_1, s2_1, e2_1, depth + 1, value | (1 << bit_size - depth - 1)));
}
}
return intersection;
};
private:
uint64_t get_num_of_bit(uint64_t x) {
if (x == 0) return 0;
x--;
uint64_t bit_num = 0;
while (x >> bit_num) {
++bit_num;
}
return bit_num;
}
};
using namespace std;
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
int N;
cin >> N;
vector<uint64_t> A(N);
FOR(i, 0, N) {
cin >> A[i];
}
DynamicWaveletMatrix dwm(100010, A);
int last_ans = 0;
int Q;
cin >> Q;
FOR(i, 0, Q) {
int m, l, r, k;
cin >> m >> l >> r;
l = (l + last_ans - 1) % N + 1;
r = (r + last_ans - 1) % N + 1;
if (l > r) {
swap(l, r);
}
l--; r--;
if (m == 1) {
auto val = dwm.access(r);
dwm.erase(r);
dwm.insert(l, val);
}
else {
cin >> k;
k = (k + last_ans - 1) % N + 1;
auto a = dwm.rank(k, l);
auto b = dwm.rank(k, r + 1);
last_ans = b - a;
print(last_ans);
}
}
return 0;
}