結果
| 問題 |
No.2540 同値性判定
|
| ユーザー |
 CuriousFairy315
|
| 提出日時 | 2023-07-15 12:33:20 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 711 ms / 2,500 ms |
| コード長 | 48,370 bytes |
| コンパイル時間 | 4,202 ms |
| コンパイル使用メモリ | 101,968 KB |
| 実行使用メモリ | 65,800 KB |
| 最終ジャッジ日時 | 2024-10-08 06:42:33 |
| 合計ジャッジ時間 | 35,830 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 36 TLE * 1 |
ソースコード
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.BitSet;
import java.util.HashSet;
import java.util.NoSuchElementException;
public class Main {
public static void main(String[] args) {
new Main();
}
public Main() {
InputChecker ic = new InputChecker(System.in);
java.io.PrintWriter out = new java.io.PrintWriter(System.out);
solve(ic, out);
out.flush();
}
/*
* 命題変数の真偽を一つ固定する。
* この時、どの命題についてもその命題が真か偽かは確定する。
* 命題をfとすると、f(P0, …, P5)=命題の真偽、という形
*
* さて、この時に各演算がどのように作用するか考える。
* OYが確定していることから、ある関数g_{Ox}(f)が存在して、g_{Ox}(f) = fOxとなる
* f, xの真偽は0と1の二通りだから、g_{Ox}は2次元ベクトルとなり、このようなものは4状態しか取らないね
* ところで変換行列ってモノイドで、合成可能ですね
*/
enum Operator {
LAND, LOR, RIGHTARROW;
/**
* 命題と論理演算から定まる作用関数を返します。
* @param Y この時点でのX_hの値
* @return 作用関数
*/
BitFunction getFunction(long val) {
switch(this) {
case LAND:
return BitFunction.and(val);
case LOR:
return BitFunction.or(val);
case RIGHTARROW:
return BitFunction.imply(val);
}
throw new AssertionError();
}
static Operator getOperator(String operator) {
switch(operator) {
case "land":
return Operator.LAND;
case "lor":
return Operator.LOR;
case "Rightarrow":
return Operator.RIGHTARROW;
}
throw new AssertionError();
}
}
class Query {
int h;
Operator o;
int l, r, l2, r2;
Query(InputChecker ic, int N) {
h = ic.nextInt(0, N - 1);
ic.nextChar(' ');
o = Operator.getOperator(ic.next(CharSet.ALPHABET));
ic.nextChar(' ');
l = ic.nextInt(0, N - 1);
ic.nextChar(' ');
r = ic.nextInt(l, N - 1) + 1;
ic.nextChar(' ');
l2 = ic.nextInt(0, N - 1);
ic.nextChar(' ');
r2 = ic.nextInt(l2, N - 1) + 1;
// if (r2 - l2 > 1000) throw new AssertionError();
ic.readNewLine();
}
}
/*
* 基本方針
* 1. 全体の命題変数の真偽をそれぞれ固定し、その場合の真偽を解く
* 従って、同じ問題を2^6 = 64回解くことになる
*
* 命題変数が決め打たれている時、真偽も分かるので0,1の2状態のみ管理すれば良い
* すると、問題は以下の様に考えることができる
*
* 0,1で表された長さNの配列が与えられます
* 以下のクエリを捌いてください
* 1. X_hの値を取得し、X_h及び追加で与えられた文字列oに応じてどれかの区間作用が発生する
* ・区間を0にする
* ・区間を1にする
* ・区間を反転する
* 2. 区間のそれぞれの0,1の値を取得する、長さは最大でL
*
* さて、区間作用1点取得のクエリをO(A)/O(B)で捌けるとすると、計算量はクエリごとにO(A+LB)
* また、区間作用1点取得といえばセグ木や平方分割が有名だが、セグ木だとO(LlogN)、平方分割だとO(L+√N)
* ここでLは√Nより大きい(10^3)から、平方分割を書いた方が得か
*
* 作用だが、作用行列を考えれば4状態あれば十分であることが分かる
* 0の時にxを返す、1の時にyを返すを持った行列(x, y)に対して作用を考えると、全部作用行列になるので
* (0, 0)=0, (0, 1)=e, (1, 0)=~, (1, 1)=1として表す
* この時、左辺を左、右辺を上に書く行列だと以下の様になる
* \ 0 1 e ~
* 0 0 0 0 0
* 1 1 1 1 1
* e 0 1 e ~
* ~ 1 0 ~ e
* さて、これを良い感じにエンコードしたい
*
* この方針だとTLEするか……ちゃんと64並列で解こうね
*
* ということで、ちゃんとand, or, notを解く
* xに対して作用する関数f_{a, b}=(x&a)^bを定義
* この時、結果は以下の様になる
* (0, 0)→0
* (0, 1)→1
* (1, 0)→x
* (1, 1)→!x
* つまり、全てのパターンを網羅している
* g_{c, d}∘f_{a, b} = h_{a&c, (b&c)^d}で合成関数も定義できるので勝ち
*/
public void solve(InputChecker ic, java.io.PrintWriter out) {
int N = ic.nextInt(1, 1_000_000);
ic.nextChar(' ');
int Q = ic.nextInt(1, 100_000);
ic.readNewLine();
Query[] query = new Query[Q];
for (int i = 0;i < Q;++ i) query[i] = new Query(ic, N);
ic.checkEOF();
BitSet ans = solve(N, query);
for (int i = 0;i < Q;++ i) {
out.println(ans.get(i) ? "Yes" : "No");
}
}
static final int c = 6; // 命題変数の種類
/**
* 命題変数の真偽をPを用いて定めた時の結果をqueryに格納します。
* @param N 配列長
* @param query クエリ
* @return 答えを格納したBitSet
*/
BitSet solve(int N, Query[] query) {
LongDualSqrtDecomposition<BitFunction> X;
{
long[] x = new long[N];
long[] test = new long[c];
for (int i = 0;i < c;++ i) {
for (int j = 0;j < 64;++ j) if ((j >> i & 1) != 0) test[i] |= 1L << j;
}
for (int i = 0;i < N;++ i) x[i] = test[i % c];
X = LongDualSqrtDecomposition.create(x, BitFunction.composition());
}
BitSet result = new BitSet(query.length);
for (int i = 0;i < query.length;++ i) {
Query q = query[i];
BitFunction operator = q.o.getFunction(X.get(q.h)); // 今回の演算
X.apply(q.l, q.r, operator);
HashSet<Long> set = new HashSet<>(q.r2 - q.l2, 1);
X.foreach(q.l2, q.r2, (j, v) -> set.add(v));
result.set(i, set.size() != q.r2 - q.l2);
}
return result;
}
public static int exponent10(int n, int e) {
return n * pow(10, e);
}
public static long exponent10L(int n, int e) {
return n * pow(10L, e);
}
public static int pow(int a, int b) {
int ans = 1;
for (int mul = a;b > 0;b >>= 1, mul *= mul) if ((b & 1) != 0) ans *= mul;
return ans;
}
public static long pow(long a, long b) {
long ans = 1;
for (long mul = a;b > 0;b >>= 1, mul *= mul) if ((b & 1) != 0) ans *= mul;
return ans;
}
public static class CharSet {
private final BitSet set = new BitSet(256);
public void add(char... c) {
for (char i : c) set.set(i);
}
public void add(CharSet... s) {
for (CharSet i : s) set.or(i.set);
}
public boolean contains(char... c) {
for (char i : c) if (!set.get(i)) return false;
return true;
}
public boolean contains(String s) {
return contains(s.toCharArray());
}
private static final class Chars extends CharSet {
public Chars(char... c) {
super.add(c);
}
public Chars(CharSet... s) {
super.add(s);
}
@Override
public void add(char... c) {
throw new UnsupportedOperationException();
}
@Override
public void add(CharSet... s) {
throw new UnsupportedOperationException();
}
}
public static final CharSet NUMBER = new Chars('0','1','2','3','4','5','6','7','8','9');
public static final CharSet LOWER = new Chars('a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z');
public static final CharSet UPPER = new Chars('A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z');
public static final CharSet ALPHABET = new Chars(LOWER, UPPER);
}
public static class InputChecker {
private InputStream in;
private final byte[] buffer = new byte[1024];
private final byte[] undo = new byte[1024];
private int undoSize = 0;
private int read = 0;
private int length = 0;
public InputChecker(InputStream in) {
this.in = in;
}
public final void setInputStream(InputStream in) {
this.in = in;
}
public final void setInputStream(File in) {
try {
this.in = new FileInputStream(in);
} catch (FileNotFoundException e) {
e.printStackTrace();
}
}
private boolean hasNextByte() {
if (undoSize > 0) return true;
if (read < length) return true;
read = 0;
try {
length = in.read(buffer);
} catch (IOException e) {
e.printStackTrace();
}
return length > 0;
}
private byte readByte() {
if (hasNextByte()) return undoSize > 0 ? undo[--undoSize] : buffer[read++];
throw new NoSuchElementException();
}
private void undo(byte b) {
undo[undoSize ++] = b;
}
private void undo(char c) {
if ((c & 0xFF80) == 0) {
undo((byte)c);
return;
}
undo((byte)(c & 0x3F | 0x80));
if ((c & 0xF800) == 0) {
undo((byte)(c >> 6 & 0x1F | 0xC0));
} else {
undo((byte)(c >> 6 & 0x3F | 0x80));
undo((byte)(c >> 12 | 0xE0));
}
}
public final boolean hasNext() {
return hasNextByte();
}
public final char nextChar() {
byte b = readByte();
if ((b & 0x80) == 0) return (char)b;
if ((b & 0x20) == 0) return (char)((b & 0x1F) << 6 | readByte() & 0x3F);
return (char)((b & 0xF) << 12 | (readByte() & 0x3F) << 6 | readByte() & 0x3F);
}
public final char nextChar(char estimate) {
char c = nextChar();
if (estimate == c) return estimate;
undo(c);
throw new AssertionError();
}
public final char nextChar(CharSet estimate) {
char c = nextChar();
if (estimate.contains(c)) return c;
undo(c);
throw new AssertionError();
}
public final void readNewLine() {
char c = nextChar();
if (c == '\r') {
c = nextChar();
if (c != '\n') undo(c);
return;
} else if (c == '\n') return;
undo(c);
throw new AssertionError();
}
public final void checkEOF() {
if (hasNextByte()) throw new AssertionError();
}
public final String next(CharSet contains) {
StringBuilder sb = new StringBuilder();
try {
do {
char c = nextChar();
if (!contains.contains(c)) {
undo(c);
return sb.toString();
}
sb.append(c);
} while(true);
} catch (NoSuchElementException e) {
if (sb.length() <= 0) throw new AssertionError();
return sb.toString();
}
}
public final int nextInt() {
byte b = readByte();
int n = 0;
if (b == '-') {
if (!isNumber(b = readByte())) {
undo(b);
throw new NumberFormatException();
}
try {
if (b == '0') {
if (!isNumber(b = readByte())) {
undo(b);
return 0;
}
throw new NumberFormatException();
}
do n = Math.addExact(Math.multiplyExact(n, 10), '0' - b); while(isNumber(b = readByte()));
undo(b);
} catch (NoSuchElementException e) {
}
return n;
}
if (!isNumber(b)) {
undo(b);
throw new NumberFormatException();
}
try {
if (b == '0') {
if (!isNumber(b = readByte())) {
undo(b);
return 0;
}
throw new NumberFormatException();
}
do n = Math.addExact(Math.multiplyExact(n, 10), b - '0'); while(isNumber(b = readByte()));
undo(b);
} catch (NoSuchElementException e) {
}
return n;
}
public final int nextInt(int min, int max) {
int n = nextInt();
if (min <= n && n <= max) return n;
throw new NumberFormatException();
}
private static boolean isNumber(byte c) {
return '0' <= c && c <= '9';
}
public final long nextLong() {
byte b = readByte();
long n = 0;
if (b == '-') {
if (!isNumber(b = readByte())) {
undo(b);
throw new NumberFormatException();
}
try {
if (b == '0') {
if (!isNumber(b = readByte())) {
undo(b);
return 0;
}
throw new NumberFormatException();
}
do n = Math.addExact(Math.multiplyExact(n, 10), '0' - b); while(isNumber(b = readByte()));
undo(b);
} catch (NoSuchElementException e) {
}
return n;
}
if (!isNumber(b)) {
undo(b);
throw new NumberFormatException();
}
try {
if (b == '0') {
if (!isNumber(b = readByte())) {
undo(b);
return 0;
}
throw new NumberFormatException();
}
do n = Math.addExact(Math.multiplyExact(n, 10), b - '0'); while(isNumber(b = readByte()));
undo(b);
} catch (NoSuchElementException e) {
}
return n;
}
public final long nextLong(long min, long max) {
long n = nextLong();
if (min <= n && n <= max) return n;
throw new NumberFormatException();
}
public final double nextDouble() {
StringBuilder sb = new StringBuilder();
byte b = readByte();
if (b == '-') {
sb.append(b);
b = readByte();
}
if (b == '0') {
sb.append(b);
b = readByte();
} else {
while(isNumber(b)) {
sb.append(b);
b = readByte();
}
}
if (b == '.') {
sb.append(b);
b = readByte();
while(isNumber(b)) {
sb.append(b);
b = readByte();
}
}
if (b == 'e' || b == 'E') {
sb.append(b);
b = readByte();
if (b == '-' || b == '+') {
sb.append(b);
b = readByte();
}
while(isNumber(b)) {
sb.append(b);
b = readByte();
}
}
undo(b);
return Double.parseDouble(sb.toString());
}
}
}
class BitFunction implements LongEndoMorphism {
final long and, xor;
private BitFunction(long and, long xor) {
this.and = and;
this.xor = xor;
}
@Override
public long applyAsLong(long operand) {
return operand & and ^ xor;
}
public BitFunction andThen(BitFunction after) {
return new BitFunction(and & after.and, xor & after.and ^ after.xor);
}
public BitFunction compose(BitFunction before) {
return new BitFunction(before.and & and, before.xor & and ^ xor);
}
public static BitFunction identity() {
return new BitFunction(-1L, 0L);
}
public static Monoid<BitFunction> composition() {
return new Monoid<BitFunction>() {
@Override
public BitFunction apply(BitFunction t, BitFunction u) {
return u.andThen(t);
}
@Override
public BitFunction identity() {
return BitFunction.identity();
}
};
}
public static BitFunction and(long and) {
return new BitFunction(and, 0L);
}
public static BitFunction xor(long xor) {
return new BitFunction(-1L, xor);
}
public static BitFunction or(long or) {
return new BitFunction(~or, or);
}
public static BitFunction not() {
return new BitFunction(-1L, -1L);
}
public static BitFunction nand(long and) {
return new BitFunction(and, -1L);
}
public static BitFunction nor(long or) {
return new BitFunction(~or, ~or);
}
public static BitFunction imply(long consequent) {
return new BitFunction(~consequent, -1L);
}
public static BitFunction xnor(long xor) {
return new BitFunction(-1L, ~xor);
}
}
class LongDualSqrtDecomposition<M extends LongEndoMorphism> {
private final Monoid<M> composition;
private final int bucket;
private final Object[] top;
private final long[] bottom;
private final M identity;
LongDualSqrtDecomposition(long[] array, Monoid<M> composition, int bucket) {
this.composition = composition;
identity = composition.identity();
bottom = array.clone();
top = new Object[array.length / bucket];
Arrays.fill(top, identity);
this.bucket = bucket;
}
@SuppressWarnings("unchecked")
private M getTop(int index) {
return (M) top[index];
}
private void lazy(int topIndex) {
if (0 > topIndex || topIndex >= top.length) return;
M apply = getTop(topIndex);
top[topIndex] = identity;
for (int l = topIndex * bucket, r = l + bucket;l < r;++ l) bottom[l] = apply.applyAsLong(bottom[l]);
}
public void apply(int p, M f) {
lazy(p / bucket);
bottom[p] = f.applyAsLong(bottom[p]);
}
public void apply(int l, int r, M f) {
int lTop = (l + bucket - 1) / bucket;
int rTop = r / bucket;
if (lTop >= rTop) {
if (lTop == rTop) lazy(lTop - 1);
lazy(rTop);
for (int i = l;i < r;++ i) bottom[i] = f.applyAsLong(bottom[i]);
return;
}
int rBottom = lTop * bucket;
int lBottom = rTop * bucket;
lazy(lTop - 1);
lazy(rTop);
for (int i = l;i < rBottom;++ i) bottom[i] = f.applyAsLong(bottom[i]);
for (int i = lBottom;i < r;++ i) bottom[i] = f.applyAsLong(bottom[i]);
for (int i = lTop;i < rTop;++ i) top[i] = composition.apply(f, getTop(i));
}
public void set(int p, long val) {
lazy(p / bucket);
bottom[p] = val;
}
public long get(int p) {
lazy(p / bucket);
return bottom[p];
}
public long[] get(int l, int r) {
int lTop = l / bucket;
int rTop = (r + bucket - 1) / bucket;
for (int i = lTop;i < rTop;++ i) lazy(i);
return Arrays.copyOfRange(bottom, l, r);
}
public void foreach(int l, int r, LongIndexableConsumer action) {
int lTop = l / bucket;
int rTop = (r + bucket - 1) / bucket;
for (int i = lTop;i < rTop;++ i) lazy(i);
for (int i = l;i < r;++ i) action.accept(i, bottom[i]);
}
public static <M extends LongEndoMorphism> LongDualSqrtDecomposition<M> create(long[] array, Monoid<M> composition, int bucket) {
return new LongDualSqrtDecomposition<>(array, composition, bucket);
}
public static <M extends LongEndoMorphism> LongDualSqrtDecomposition<M> create(long[] array, Monoid<M> composition) {
return new LongDualSqrtDecomposition<>(array, composition, (int)Math.max(1, Math.sqrt(array.length * 2) / 2));
}
}
interface IndexableConsumer<E> {
public void accept(int index, E value);
}
interface IntIndexableConsumer extends IndexableConsumer<Integer> {
public void acceptAsInt(int index, int value);
@Override
public default void accept(int index, Integer value) {
acceptAsInt(index, value);
}
}
interface LongIndexableConsumer extends IndexableConsumer<Long> {
public void acceptAsLong(int index, long value);
@Override
public default void accept(int index, Long value) {
acceptAsLong(index, value);
}
}
interface DoubleIndexableConsumer extends IndexableConsumer<Double> {
public void acceptAsDouble(int index, double value);
@Override
public default void accept(int index, Double value) {
acceptAsDouble(index, value);
}
}
interface LongMonoid extends Monoid<Long>, LongAssociative, LongUnital {
@Override
public default long hyperAsLong(long element, int repeat) {
if (repeat < 0) throw new IllegalArgumentException("undefined operation");
long ret = identityAsLong();
for (long mul = element;repeat > 0;repeat >>= 1, mul = applyAsLong(mul, mul)) if ((repeat & 1) != 0) ret = applyAsLong(ret, mul);
return ret;
}
@Override
public default long hyperAsLong(long element, long repeat) {
if (repeat < 0) throw new IllegalArgumentException("undefined operation");
long ret = identityAsLong();
for (long mul = element;repeat > 0;repeat >>= 1, mul = applyAsLong(mul, mul)) if ((repeat & 1) != 0) ret = applyAsLong(ret, mul);
return ret;
}
@Override
default Long hyper(Long element, int repeat) {
return hyperAsLong(element, repeat);
}
@Override
default Long hyper(Long element, long repeat) {
return hyperAsLong(element, repeat);
}
}
interface LongEndoMorphism extends LongMorphism, EndoMorphism<Long>, java.util.function.LongUnaryOperator {
@Override
public default Long apply(Long operand) {
return applyAsLong((long) operand);
}
@Override
public default Long apply(long operand) {
return applyAsLong(operand);
}
@Override
public default long applyAsLong(Long operand) {
return applyAsLong((long) operand);
}
public default LongEndoMorphism andThen(LongEndoMorphism after) {
return s -> after.applyAsLong(applyAsLong(s));
}
public default LongEndoMorphism compose(LongEndoMorphism before) {
return s -> applyAsLong(before.applyAsLong(s));
}
public static LongEndoMorphism identity() {
return t -> t;
}
public static Monoid<LongEndoMorphism> composition() {
return new Monoid<LongEndoMorphism>() {
@Override
public LongEndoMorphism apply(LongEndoMorphism t, LongEndoMorphism u) {
return u.andThen(t);
}
@Override
public LongEndoMorphism identity() {
return LongEndoMorphism.identity();
}
};
}
}
interface Monoid<T> extends Associative<T>, Unital<T> {
@Override
public default T hyper(T element, int repeat) {
if (repeat < 0) throw new IllegalArgumentException("undefined operation");
T ret = identity();
for (T mul = element;repeat > 0;repeat >>= 1, mul = apply(mul, mul)) if ((repeat & 1) != 0) ret = apply(ret, mul);
return ret;
}
@Override
public default T hyper(T element, long repeat) {
if (repeat < 0) throw new IllegalArgumentException("undefined operation");
T ret = identity();
for (T mul = element;repeat > 0;repeat >>= 1, mul = apply(mul, mul)) if ((repeat & 1) != 0) ret = apply(ret, mul);
return ret;
}
}
interface LongAssociative extends Associative<Long>, LongMagma{
@Override
public default Long apply(Long t, Long u) {
return applyAsLong(t, u);
}
@Override
public default Long hyper(Long element, int repeat) {
return hyperAsLong(element, repeat);
}
@Override
public default Long hyper(Long element, long repeat) {
return hyperAsLong(element, repeat);
}
public default long hyperAsLong(long element, int repeat) {
if (repeat < 1) throw new IllegalArgumentException("undefined operation");
long ret = element;
-- repeat;
for (long mul = element;repeat > 0;repeat >>= 1, mul = applyAsLong(mul, mul)) if ((repeat & 1) != 0) ret = applyAsLong(ret, mul);
return ret;
}
public default long hyperAsLong(long element, long repeat) {
if (repeat < 1) throw new IllegalArgumentException("undefined operation");
long ret = element;
-- repeat;
for (long mul = element;repeat > 0;repeat >>= 1, mul = applyAsLong(mul, mul)) if ((repeat & 1) != 0) ret = applyAsLong(ret, mul);
return ret;
}
}
interface LongUnital extends Unital<Long>, LongMagma {
@Override
public default Long identity() {
return identityAsLong();
}
public long identityAsLong();
}
interface EndoMorphism<T> extends Morphism<T, T>, java.util.function.UnaryOperator<T> {
public default EndoMorphism<T> andThen(EndoMorphism<T> after) {
return s -> after.apply(apply(s));
}
public default EndoMorphism<T> compose(EndoMorphism<T> before) {
return s -> apply(before.apply(s));
}
public static <T> EndoMorphism<T> identity() {
return t -> t;
}
public static <T> Monoid<EndoMorphism<T>> composition() {
return new Monoid<EndoMorphism<T>>() {
@Override
public EndoMorphism<T> apply(EndoMorphism<T> t, EndoMorphism<T> u) {
return u.andThen(t);
}
@Override
public EndoMorphism<T> identity() {
return EndoMorphism.identity();
}
};
}
}
interface LongMorphism
extends LongToObjMorphism<Long>, ObjToLongMorphism<Long>, java.util.function.LongUnaryOperator {
@Override
public default Long apply(Long operand) {
return applyAsLong((long) operand);
}
@Override
public default Long apply(long operand) {
return applyAsLong(operand);
}
@Override
public default long applyAsLong(Long operand) {
return applyAsLong((long) operand);
}
@Override
public default LongToIntMorphism andThen(java.util.function.LongToIntFunction after) {
return s -> after.applyAsInt(applyAsLong(s));
}
@Override
public default LongMorphism andThen(java.util.function.LongUnaryOperator after) {
return s -> after.applyAsLong(applyAsLong(s));
}
public default LongMorphism andThen(LongMorphism after) {
return s -> after.applyAsLong(applyAsLong(s));
}
@Override
public default LongToDoubleMorphism andThen(java.util.function.LongToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsLong(s));
}
@Override
public default <T> LongToObjMorphism<T> andThen(java.util.function.LongFunction<? extends T> after) {
return s -> after.apply(applyAsLong(s));
}
@Override
public default IntToLongMorphism compose(java.util.function.IntToLongFunction before) {
return s -> applyAsLong(before.applyAsLong(s));
}
@Override
public default LongMorphism compose(java.util.function.LongUnaryOperator before) {
return s -> applyAsLong(before.applyAsLong(s));
}
public default LongMorphism compose(LongMorphism before) {
return s -> applyAsLong(before.applyAsLong(s));
}
@Override
public default DoubleToLongMorphism compose(java.util.function.DoubleToLongFunction before) {
return s -> applyAsLong(before.applyAsLong(s));
}
@Override
public default <S> ObjToLongMorphism<S> compose(java.util.function.ToLongFunction<? super S> before) {
return s -> applyAsLong(before.applyAsLong(s));
}
public static Associative<LongMorphism> composition() {
return (t, u) -> t.andThen(u);
}
}
interface Associative<T> extends Magma<T> {
public default T hyper(T element, int repeat) {
if (repeat < 1) throw new IllegalArgumentException("undefined operation");
T ret = element;
--repeat;
for (T mul = element; repeat > 0; repeat >>= 1, mul = apply(mul, mul))
if ((repeat & 1) != 0) ret = apply(ret, mul);
return ret;
}
public default T hyper(T element, long repeat) {
if (repeat < 1) throw new IllegalArgumentException("undefined operation");
T ret = element;
--repeat;
for (T mul = element; repeat > 0; repeat >>= 1, mul = apply(mul, mul))
if ((repeat & 1) != 0) ret = apply(ret, mul);
return ret;
}
}
interface Unital<T> extends Magma<T> {
public T identity();
}
interface LongMagma extends Magma<Long>, java.util.function.LongBinaryOperator {
@Override
public default EndoMorphism<Long> partial(Long bind) {
return partialAsLong(bind);
}
public default LongEndoMorphism partialAsLong(long bind) {
return t -> applyAsLong(bind, t);
}
}
interface Morphism<S, T> extends java.util.function.Function<S, T>{
@Override
public default <U> Morphism<S, U> andThen(java.util.function.Function<? super T, ? extends U> after) {
return s -> after.apply(apply(s));
}
@Override
public default <U> Morphism<U,T> compose(java.util.function.Function<? super U,? extends S> before) {
return s -> apply(before.apply(s));
}
public static <T> Associative<Morphism<? super T, T>> composition() {
return (t, u) -> t.andThen(u);
}
}
interface LongToObjMorphism<T> extends Morphism<Long, T>, java.util.function.LongFunction<T> {
@Override
public default T apply(Long operand) {
return apply((long) operand);
}
public default LongToIntMorphism andThen(java.util.function.ToIntFunction<? super T> after) {
return s -> after.applyAsInt(apply(s));
}
public default LongMorphism andThen(java.util.function.ToLongFunction<? super T> after) {
return s -> after.applyAsLong(apply(s));
}
public default LongToDoubleMorphism andThen(java.util.function.ToDoubleFunction<? super T> after) {
return s -> after.applyAsDouble(apply(s));
}
@Override
public default <U> LongToObjMorphism<U> andThen(java.util.function.Function<? super T, ? extends U> after) {
return s -> after.apply(apply(s));
}
public default IntToObjMorphism<T> compose(java.util.function.IntToLongFunction before) {
return s -> apply(before.applyAsLong(s));
}
public default LongToObjMorphism<T> compose(java.util.function.LongUnaryOperator before) {
return s -> apply(before.applyAsLong(s));
}
public default DoubleToObjMorphism<T> compose(java.util.function.DoubleToLongFunction before) {
return s -> apply(before.applyAsLong(s));
}
public default <S> Morphism<S, T> compose(java.util.function.ToLongFunction<? super S> before) {
return s -> apply(before.applyAsLong(s));
}
}
interface ObjToLongMorphism<S> extends Morphism<S, Long>, java.util.function.ToLongFunction<S> {
@Override
public default Long apply(S operand) {
return applyAsLong(operand);
}
public default ObjToIntMorphism<S> andThen(java.util.function.LongToIntFunction after) {
return s -> after.applyAsInt(applyAsLong(s));
}
public default ObjToLongMorphism<S> andThen(java.util.function.LongUnaryOperator after) {
return s -> after.applyAsLong(applyAsLong(s));
}
public default ObjToDoubleMorphism<S> andThen(java.util.function.LongToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsLong(s));
}
public default <T> Morphism<S, T> andThen(java.util.function.LongFunction<? extends T> after) {
return s -> after.apply(applyAsLong(s));
}
public default IntToLongMorphism compose(java.util.function.IntFunction<? extends S> before) {
return s -> applyAsLong(before.apply(s));
}
public default LongMorphism compose(java.util.function.LongFunction<? extends S> before) {
return s -> applyAsLong(before.apply(s));
}
public default DoubleToLongMorphism compose(java.util.function.DoubleFunction<? extends S> before) {
return s -> applyAsLong(before.apply(s));
}
@Override
public default <U> ObjToLongMorphism<U> compose(java.util.function.Function<? super U, ? extends S> before) {
return s -> applyAsLong(before.apply(s));
}
}
interface LongToIntMorphism
extends LongToObjMorphism<Integer>, ObjToIntMorphism<Long>, java.util.function.LongToIntFunction {
@Override
public default Integer apply(Long operand) {
return applyAsInt((long) operand);
}
@Override
public default Integer apply(long operand) {
return applyAsInt(operand);
}
@Override
public default int applyAsInt(Long operand) {
return applyAsInt((long) operand);
}
@Override
public default LongToIntMorphism andThen(java.util.function.IntUnaryOperator after) {
return s -> after.applyAsInt(applyAsInt(s));
}
@Override
public default LongMorphism andThen(java.util.function.IntToLongFunction after) {
return s -> after.applyAsLong(applyAsInt(s));
}
@Override
public default LongToDoubleMorphism andThen(java.util.function.IntToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsInt(s));
}
@Override
public default <T> LongToObjMorphism<T> andThen(java.util.function.IntFunction<? extends T> after) {
return s -> after.apply(applyAsInt(s));
}
@Override
public default IntMorphism compose(java.util.function.IntToLongFunction before) {
return s -> applyAsInt(before.applyAsLong(s));
}
@Override
public default LongToIntMorphism compose(java.util.function.LongUnaryOperator before) {
return s -> applyAsInt(before.applyAsLong(s));
}
@Override
public default DoubleToIntMorphism compose(java.util.function.DoubleToLongFunction before) {
return s -> applyAsInt(before.applyAsLong(s));
}
@Override
public default <S> ObjToIntMorphism<S> compose(java.util.function.ToLongFunction<? super S> before) {
return s -> applyAsInt(before.applyAsLong(s));
}
}
interface LongToDoubleMorphism
extends LongToObjMorphism<Double>, ObjToDoubleMorphism<Long>, java.util.function.LongToDoubleFunction {
@Override
public default Double apply(Long operand) {
return applyAsDouble((long) operand);
}
@Override
public default Double apply(long operand) {
return applyAsDouble(operand);
}
@Override
public default double applyAsDouble(Long operand) {
return applyAsDouble((long) operand);
}
@Override
public default LongToIntMorphism andThen(java.util.function.DoubleToIntFunction after) {
return s -> after.applyAsInt(applyAsDouble(s));
}
@Override
public default LongMorphism andThen(java.util.function.DoubleToLongFunction after) {
return s -> after.applyAsLong(applyAsDouble(s));
}
@Override
public default LongToDoubleMorphism andThen(java.util.function.DoubleUnaryOperator after) {
return s -> after.applyAsDouble(applyAsDouble(s));
}
@Override
public default <T> LongToObjMorphism<T> andThen(java.util.function.DoubleFunction<? extends T> after) {
return s -> after.apply(applyAsDouble(s));
}
@Override
public default IntToDoubleMorphism compose(java.util.function.IntToLongFunction before) {
return s -> applyAsDouble(before.applyAsLong(s));
}
@Override
public default LongToDoubleMorphism compose(java.util.function.LongUnaryOperator before) {
return s -> applyAsDouble(before.applyAsLong(s));
}
@Override
public default DoubleMorphism compose(java.util.function.DoubleToLongFunction before) {
return s -> applyAsDouble(before.applyAsLong(s));
}
@Override
public default <S> ObjToDoubleMorphism<S> compose(java.util.function.ToLongFunction<? super S> before) {
return s -> applyAsDouble(before.applyAsLong(s));
}
}
interface IntToLongMorphism
extends IntToObjMorphism<Long>, ObjToLongMorphism<Integer>, java.util.function.IntToLongFunction {
@Override
public default Long apply(Integer operand) {
return applyAsLong((int) operand);
}
@Override
public default Long apply(int operand) {
return applyAsLong(operand);
}
@Override
public default long applyAsLong(Integer operand) {
return applyAsLong((int) operand);
}
@Override
public default IntMorphism andThen(java.util.function.LongToIntFunction after) {
return s -> after.applyAsInt(applyAsLong(s));
}
@Override
public default IntToLongMorphism andThen(java.util.function.LongUnaryOperator after) {
return s -> after.applyAsLong(applyAsLong(s));
}
@Override
public default IntToDoubleMorphism andThen(java.util.function.LongToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsLong(s));
}
@Override
public default <T> IntToObjMorphism<T> andThen(java.util.function.LongFunction<? extends T> after) {
return s -> after.apply(applyAsLong(s));
}
@Override
public default IntToLongMorphism compose(java.util.function.IntUnaryOperator before) {
return s -> applyAsLong(before.applyAsInt(s));
}
@Override
public default LongMorphism compose(java.util.function.LongToIntFunction before) {
return s -> applyAsLong(before.applyAsInt(s));
}
@Override
public default DoubleToLongMorphism compose(java.util.function.DoubleToIntFunction before) {
return s -> applyAsLong(before.applyAsInt(s));
}
@Override
public default <S> ObjToLongMorphism<S> compose(java.util.function.ToIntFunction<? super S> before) {
return s -> applyAsLong(before.applyAsInt(s));
}
}
interface DoubleToLongMorphism
extends DoubleToObjMorphism<Long>, ObjToLongMorphism<Double>, java.util.function.DoubleToLongFunction {
@Override
public default Long apply(Double operand) {
return applyAsLong((double) operand);
}
@Override
public default Long apply(double operand) {
return applyAsLong(operand);
}
@Override
public default long applyAsLong(Double operand) {
return applyAsLong((double) operand);
}
@Override
public default DoubleToIntMorphism andThen(java.util.function.LongToIntFunction after) {
return s -> after.applyAsInt(applyAsLong(s));
}
@Override
public default DoubleToLongMorphism andThen(java.util.function.LongUnaryOperator after) {
return s -> after.applyAsLong(applyAsLong(s));
}
@Override
public default DoubleMorphism andThen(java.util.function.LongToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsLong(s));
}
@Override
public default <T> DoubleToObjMorphism<T> andThen(java.util.function.LongFunction<? extends T> after) {
return s -> after.apply(applyAsLong(s));
}
@Override
public default IntToLongMorphism compose(java.util.function.IntToDoubleFunction before) {
return s -> applyAsLong(before.applyAsDouble(s));
}
@Override
public default LongMorphism compose(java.util.function.LongToDoubleFunction before) {
return s -> applyAsLong(before.applyAsDouble(s));
}
@Override
public default DoubleToLongMorphism compose(java.util.function.DoubleUnaryOperator before) {
return s -> applyAsLong(before.applyAsDouble(s));
}
@Override
public default <S> ObjToLongMorphism<S> compose(java.util.function.ToDoubleFunction<? super S> before) {
return s -> applyAsLong(before.applyAsDouble(s));
}
}
interface Magma<T> extends java.util.function.BinaryOperator<T>{
public default EndoMorphism<T> partial(T bind) {
return t -> apply(bind, t);
}
}
interface IntToObjMorphism<T> extends Morphism<Integer, T>, java.util.function.IntFunction<T> {
@Override
public default T apply(Integer operand) {
return apply((int) operand);
}
public default IntMorphism andThen(java.util.function.ToIntFunction<? super T> after) {
return s -> after.applyAsInt(apply(s));
}
public default IntToLongMorphism andThen(java.util.function.ToLongFunction<? super T> after) {
return s -> after.applyAsLong(apply(s));
}
public default IntToDoubleMorphism andThen(java.util.function.ToDoubleFunction<? super T> after) {
return s -> after.applyAsDouble(apply(s));
}
@Override
public default <U> IntToObjMorphism<U> andThen(java.util.function.Function<? super T, ? extends U> after) {
return s -> after.apply(apply(s));
}
public default IntToObjMorphism<T> compose(java.util.function.IntUnaryOperator before) {
return s -> apply(before.applyAsInt(s));
}
public default LongToObjMorphism<T> compose(java.util.function.LongToIntFunction before) {
return s -> apply(before.applyAsInt(s));
}
public default DoubleToObjMorphism<T> compose(java.util.function.DoubleToIntFunction before) {
return s -> apply(before.applyAsInt(s));
}
public default <S> Morphism<S, T> compose(java.util.function.ToIntFunction<? super S> before) {
return s -> apply(before.applyAsInt(s));
}
}
interface DoubleToObjMorphism<T> extends Morphism<Double, T>, java.util.function.DoubleFunction<T> {
@Override
public default T apply(Double operand) {
return apply((double) operand);
}
public default DoubleToIntMorphism andThen(java.util.function.ToIntFunction<? super T> after) {
return s -> after.applyAsInt(apply(s));
}
public default DoubleToLongMorphism andThen(java.util.function.ToLongFunction<? super T> after) {
return s -> after.applyAsLong(apply(s));
}
public default DoubleMorphism andThen(java.util.function.ToDoubleFunction<? super T> after) {
return s -> after.applyAsDouble(apply(s));
}
@Override
public default <U> DoubleToObjMorphism<U> andThen(java.util.function.Function<? super T, ? extends U> after) {
return s -> after.apply(apply(s));
}
public default IntToObjMorphism<T> compose(java.util.function.IntToDoubleFunction before) {
return s -> apply(before.applyAsDouble(s));
}
public default LongToObjMorphism<T> compose(java.util.function.LongToDoubleFunction before) {
return s -> apply(before.applyAsDouble(s));
}
public default DoubleToObjMorphism<T> compose(java.util.function.DoubleUnaryOperator before) {
return s -> apply(before.applyAsDouble(s));
}
public default <S> Morphism<S, T> compose(java.util.function.ToDoubleFunction<? super S> before) {
return s -> apply(before.applyAsDouble(s));
}
}
interface ObjToIntMorphism<S> extends Morphism<S, Integer>, java.util.function.ToIntFunction<S> {
@Override
public default Integer apply(S operand) {
return applyAsInt(operand);
}
public default ObjToIntMorphism<S> andThen(java.util.function.IntUnaryOperator after) {
return s -> after.applyAsInt(applyAsInt(s));
}
public default ObjToLongMorphism<S> andThen(java.util.function.IntToLongFunction after) {
return s -> after.applyAsLong(applyAsInt(s));
}
public default ObjToDoubleMorphism<S> andThen(java.util.function.IntToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsInt(s));
}
public default <T> Morphism<S, T> andThen(java.util.function.IntFunction<? extends T> after) {
return s -> after.apply(applyAsInt(s));
}
public default IntMorphism compose(java.util.function.IntFunction<? extends S> before) {
return s -> applyAsInt(before.apply(s));
}
public default LongToIntMorphism compose(java.util.function.LongFunction<? extends S> before) {
return s -> applyAsInt(before.apply(s));
}
public default DoubleToIntMorphism compose(java.util.function.DoubleFunction<? extends S> before) {
return s -> applyAsInt(before.apply(s));
}
@Override
public default <U> ObjToIntMorphism<U> compose(java.util.function.Function<? super U, ? extends S> before) {
return s -> applyAsInt(before.apply(s));
}
}
interface ObjToDoubleMorphism<S> extends Morphism<S, Double>, java.util.function.ToDoubleFunction<S> {
@Override
public default Double apply(S operand) {
return applyAsDouble(operand);
}
public default ObjToIntMorphism<S> andThen(java.util.function.DoubleToIntFunction after) {
return s -> after.applyAsInt(applyAsDouble(s));
}
public default ObjToLongMorphism<S> andThen(java.util.function.DoubleToLongFunction after) {
return s -> after.applyAsLong(applyAsDouble(s));
}
public default ObjToDoubleMorphism<S> andThen(java.util.function.DoubleUnaryOperator after) {
return s -> after.applyAsDouble(applyAsDouble(s));
}
public default <T> Morphism<S, T> andThen(java.util.function.DoubleFunction<? extends T> after) {
return s -> after.apply(applyAsDouble(s));
}
public default IntToDoubleMorphism compose(java.util.function.IntFunction<? extends S> before) {
return s -> applyAsDouble(before.apply(s));
}
public default LongToDoubleMorphism compose(java.util.function.LongFunction<? extends S> before) {
return s -> applyAsDouble(before.apply(s));
}
public default DoubleMorphism compose(java.util.function.DoubleFunction<? extends S> before) {
return s -> applyAsDouble(before.apply(s));
}
@Override
public default <U> ObjToDoubleMorphism<U> compose(java.util.function.Function<? super U, ? extends S> before) {
return s -> applyAsDouble(before.apply(s));
}
}
interface IntMorphism
extends IntToObjMorphism<Integer>, ObjToIntMorphism<Integer>, java.util.function.IntUnaryOperator {
@Override
public default Integer apply(Integer operand) {
return applyAsInt((int) operand);
}
@Override
public default Integer apply(int operand) {
return applyAsInt(operand);
}
@Override
public default int applyAsInt(Integer operand) {
return applyAsInt((int) operand);
}
@Override
public default IntMorphism andThen(java.util.function.IntUnaryOperator after) {
return s -> after.applyAsInt(applyAsInt(s));
}
@Override
public default IntToLongMorphism andThen(java.util.function.IntToLongFunction after) {
return s -> after.applyAsLong(applyAsInt(s));
}
@Override
public default IntToDoubleMorphism andThen(java.util.function.IntToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsInt(s));
}
public default IntMorphism andThen(IntMorphism after) {
return s -> after.applyAsInt(applyAsInt(s));
}
@Override
public default <T> IntToObjMorphism<T> andThen(java.util.function.IntFunction<? extends T> after) {
return s -> after.apply(applyAsInt(s));
}
@Override
public default IntMorphism compose(java.util.function.IntUnaryOperator before) {
return s -> applyAsInt(before.applyAsInt(s));
}
@Override
public default LongToIntMorphism compose(java.util.function.LongToIntFunction before) {
return s -> applyAsInt(before.applyAsInt(s));
}
@Override
public default DoubleToIntMorphism compose(java.util.function.DoubleToIntFunction before) {
return s -> applyAsInt(before.applyAsInt(s));
}
public default IntMorphism compose(IntMorphism before) {
return s -> applyAsInt(before.applyAsInt(s));
}
@Override
public default <S> ObjToIntMorphism<S> compose(java.util.function.ToIntFunction<? super S> before) {
return s -> applyAsInt(before.applyAsInt(s));
}
public static Associative<IntMorphism> composition() {
return (t, u) -> t.andThen(u);
}
}
interface DoubleToIntMorphism
extends DoubleToObjMorphism<Integer>, ObjToIntMorphism<Double>, java.util.function.DoubleToIntFunction {
@Override
public default Integer apply(Double operand) {
return applyAsInt((double) operand);
}
@Override
public default Integer apply(double operand) {
return applyAsInt(operand);
}
@Override
public default int applyAsInt(Double operand) {
return applyAsInt((double) operand);
}
@Override
public default DoubleToIntMorphism andThen(java.util.function.IntUnaryOperator after) {
return s -> after.applyAsInt(applyAsInt(s));
}
@Override
public default DoubleToLongMorphism andThen(java.util.function.IntToLongFunction after) {
return s -> after.applyAsLong(applyAsInt(s));
}
@Override
public default DoubleMorphism andThen(java.util.function.IntToDoubleFunction after) {
return s -> after.applyAsDouble(applyAsInt(s));
}
@Override
public default <T> DoubleToObjMorphism<T> andThen(java.util.function.IntFunction<? extends T> after) {
return s -> after.apply(applyAsInt(s));
}
@Override
public default IntMorphism compose(java.util.function.IntToDoubleFunction before) {
return s -> applyAsInt(before.applyAsDouble(s));
}
@Override
public default LongToIntMorphism compose(java.util.function.LongToDoubleFunction before) {
return s -> applyAsInt(before.applyAsDouble(s));
}
@Override
public default DoubleToIntMorphism compose(java.util.function.DoubleUnaryOperator before) {
return s -> applyAsInt(before.applyAsDouble(s));
}
@Override
public default <S> ObjToIntMorphism<S> compose(java.util.function.ToDoubleFunction<? super S> before) {
return s -> applyAsInt(before.applyAsDouble(s));
}
}
interface IntToDoubleMorphism
extends IntToObjMorphism<Double>, ObjToDoubleMorphism<Integer>, java.util.function.IntToDoubleFunction {
@Override
public default Double apply(Integer operand) {
return applyAsDouble((int) operand);
}
@Override
public default Double apply(int operand) {
return applyAsDouble(operand);
}
@Override
public default double applyAsDouble(Integer operand) {
return applyAsDouble((int) operand);
}
@Override
public default IntMorphism andThen(java.util.function.DoubleToIntFunction after) {
return s -> after.applyAsInt(applyAsDouble(s));
}
@Override
public default IntToLongMorphism andThen(java.util.function.DoubleToLongFunction after) {
return s -> after.applyAsLong(applyAsDouble(s));
}
@Override
public default IntToDoubleMorphism andThen(java.util.function.DoubleUnaryOperator after) {
return s -> after.applyAsDouble(applyAsDouble(s));
}
@Override
public default <T> IntToObjMorphism<T> andThen(java.util.function.DoubleFunction<? extends T> after) {
return s -> after.apply(applyAsDouble(s));
}
@Override
public default IntToDoubleMorphism compose(java.util.function.IntUnaryOperator before) {
return s -> applyAsDouble(before.applyAsInt(s));
}
@Override
public default LongToDoubleMorphism compose(java.util.function.LongToIntFunction before) {
return s -> applyAsDouble(before.applyAsInt(s));
}
@Override
public default DoubleMorphism compose(java.util.function.DoubleToIntFunction before) {
return s -> applyAsDouble(before.applyAsInt(s));
}
@Override
public default <S> ObjToDoubleMorphism<S> compose(java.util.function.ToIntFunction<? super S> before) {
return s -> applyAsDouble(before.applyAsInt(s));
}
}
interface DoubleMorphism
extends DoubleToObjMorphism<Double>, ObjToDoubleMorphism<Double>, java.util.function.DoubleUnaryOperator {
@Override
public default Double apply(Double operand) {
return applyAsDouble((double) operand);
}
@Override
public default Double apply(double operand) {
return applyAsDouble(operand);
}
@Override
public default double applyAsDouble(Double operand) {
return applyAsDouble((double) operand);
}
@Override
public default DoubleToIntMorphism andThen(java.util.function.DoubleToIntFunction after) {
return s -> after.applyAsInt(applyAsDouble(s));
}
@Override
public default DoubleToLongMorphism andThen(java.util.function.DoubleToLongFunction after) {
return s -> after.applyAsLong(applyAsDouble(s));
}
@Override
public default DoubleMorphism andThen(java.util.function.DoubleUnaryOperator after) {
return s -> after.applyAsDouble(applyAsDouble(s));
}
public default DoubleMorphism andThen(DoubleMorphism after) {
return s -> after.applyAsDouble(applyAsDouble(s));
}
public default <T> DoubleToObjMorphism<T> andThen(DoubleToObjMorphism<? extends T> after) {
return s -> after.apply(applyAsDouble(s));
}
@Override
public default IntToDoubleMorphism compose(java.util.function.IntToDoubleFunction before) {
return s -> applyAsDouble(before.applyAsDouble(s));
}
@Override
public default LongToDoubleMorphism compose(java.util.function.LongToDoubleFunction before) {
return s -> applyAsDouble(before.applyAsDouble(s));
}
@Override
public default DoubleMorphism compose(java.util.function.DoubleUnaryOperator before) {
return s -> applyAsDouble(before.applyAsDouble(s));
}
public default DoubleMorphism compose(DoubleMorphism before) {
return s -> applyAsDouble(before.applyAsDouble(s));
}
public default <S> ObjToDoubleMorphism<S> compose(ObjToDoubleMorphism<? super S> before) {
return s -> applyAsDouble(before.applyAsDouble(s));
}
public static Associative<DoubleMorphism> composition() {
return (t, u) -> t.andThen(u);
}
}