結果

問題 No.2540 同値性判定
ユーザー CuriousFairy315CuriousFairy315
提出日時 2023-06-18 20:54:50
言語 Java21
(openjdk 21)
結果
WA  
実行時間 -
コード長 48,988 bytes
コンパイル時間 4,627 ms
コンパイル使用メモリ 100,348 KB
実行使用メモリ 142,524 KB
最終ジャッジ日時 2024-10-08 06:40:02
合計ジャッジ時間 14,016 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 83 ms
58,496 KB
testcase_01 AC 89 ms
51,616 KB
testcase_02 AC 86 ms
51,432 KB
testcase_03 AC 85 ms
51,636 KB
testcase_04 AC 87 ms
51,604 KB
testcase_05 AC 86 ms
51,604 KB
testcase_06 AC 85 ms
51,632 KB
testcase_07 AC 87 ms
51,488 KB
testcase_08 AC 87 ms
51,692 KB
testcase_09 AC 88 ms
51,696 KB
testcase_10 AC 94 ms
51,740 KB
testcase_11 WA -
testcase_12 AC 234 ms
55,600 KB
testcase_13 AC 317 ms
60,312 KB
testcase_14 AC 897 ms
65,072 KB
testcase_15 WA -
testcase_16 TLE -
testcase_17 -- -
testcase_18 -- -
testcase_19 -- -
testcase_20 -- -
testcase_21 -- -
testcase_22 -- -
testcase_23 -- -
testcase_24 -- -
evil_00.txt -- -
evil_01.txt -- -
evil_02.txt -- -
evil_03.txt -- -
evil_04.txt -- -
evil_05.txt -- -
evil_06.txt -- -
evil_07.txt -- -
evil_08.txt -- -
evil_09.txt -- -
evil_10.txt -- -
evil_11.txt -- -
権限があれば一括ダウンロードができます

ソースコード

diff #

package yukicoder_9568;

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.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
		 */
		int getFunction(boolean Y) {
			switch(this) {
				case LAND:
					return Y ? BitFunction.UNIT : BitFunction.FALSE;
				case LOR:
					return Y ? BitFunction.TRUE : BitFunction.UNIT;
				case RIGHTARROW:
					return Y ? BitFunction.TRUE : BitFunction.NOT;
			}
			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;
		long[] result;
		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;
			ic.readNewLine();
			result = new long[r2 - l2];
		}
	}

	/*
	 * 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
	 *
	 */
	public void solve(InputChecker ic, java.io.PrintWriter out) {
		int N = ic.nextInt(1, 1_000_000);
		ic.nextChar(' ');
		int Q = ic.nextInt(1, 10_000);
		ic.readNewLine();

		Query[] query = new Query[Q];
		for (int i = 0;i < Q;++ i) query[i] = new Query(ic, N);
//		ic.checkEOF();

		for (int P = 0;P < 1 << c;++ P) solve(N, query, P);
		for (Query q : query) {
//			out.println(Arrays.toString(q.result)); // TODO
			out.println(q.result.length != Arrays.stream(q.result).distinct().count() ? "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
	 * @param P Pのi-bitが命題P_iの真偽に対応する
	 */
	void solve(int N, Query[] query, int P) {
		BitSet X = new BitSet(N);
		IntDualSqrtDecomposition function = new IntDualSqrtDecomposition(N, new BitFunction(), 10);
		for (int j = 0;j < N;++ j) X.set(j, (P >> j % c & 1) != 0);
		final long test = 1L << P; // 対応するbitの位置(後で使う)
		for (Query q : query) {
			X.set(q.h, BitFunction.apply(function.poll(q.h), X.get(q.h)));
			int operator = q.o.getFunction(X.get(q.h)); // 今回の演算
			function.apply(q.l, q.r, operator);
			long[] result = q.result;
			final int l = q.l2;
			function.foreach(q.l2, q.r2, (i, f) -> {
				if (BitFunction.apply(f, X.get(i))) result[i - l] |= test;
			});
//			if (P < 4) System.out.println(P + ":" + X + "," + operator); // TODO
		}
	}

	class IntDualSqrtDecomposition {
		IntMonoid composition;
		int bucket;
		int[] top;
		int[] bottom;
		IntDualSqrtDecomposition(int length, IntMonoid composition, int bucket) {
			this.composition = composition;
			bottom = new int[length];
			Arrays.fill(bottom, composition.identityAsInt());
			top = new int[length / bucket];
			Arrays.fill(top, composition.identityAsInt());
			this.bucket = bucket;
		}
		IntDualSqrtDecomposition(int length, IntMonoid composition) {
			this(length, composition, Math.max(1, (int)Math.sqrt(length)));
		}

		private void lazy(int topIndex) {
			if (0 > topIndex || topIndex >= top.length) return;
			int apply = top[topIndex];
			top[topIndex] = composition.identityAsInt();
			for (int l = topIndex * bucket, r = l + bucket;l < r;++ l) bottom[l] = composition.applyAsInt(apply, bottom[l]);
		}

		/**
		 * p番目の要素に関数fを作用させます。
		 * @param p 作用させる要素の位置
		 * @param f 作用させる関数
		 */
		public void apply(int p, int f) {
			lazy(p / bucket);
			bottom[p] = composition.applyAsInt(f, bottom[p]);
		}

		/**
		 * 区間[l, r)に関数fを作用させます。
		 * @param l 区間の左端(これを含まない)
		 * @param r 区間の右端(これを含む)
		 * @param f 作用させる関数
		 */
		public void apply(int l, int r, int 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] = composition.applyAsInt(f, 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] = composition.applyAsInt(f, bottom[i]);
			for (int i = lBottom;i < r;++ i) bottom[i] = composition.applyAsInt(f, bottom[i]);
			for (int i = lTop;i < rTop;++ i) top[i] = composition.applyAsInt(f, top[i]);
		}


		/**
		 * p番目の要素に作用する関数をfにします。
		 * @param p 作用させる要素の位置
		 * @param f 作用させる関数
		 */
		public void set(int p, int f) {
			lazy(p / bucket);
			bottom[p] = f;
		}

		/**
		 * p番目の要素に作用する関数を取得します。
		 * @param p 取得する関数の位置
		 * @return 作用する関数
		 */
		public int get(int p) {
			lazy(p / bucket);
			return bottom[p];
		}

		/**
		 * 区間[l, r)に作用する関数を取得します。
		 * @param l 区間の左端(これを含まない)
		 * @param r 区間の右端(これを含む)
		 * @return 作用する関数
		 */
		public int[] get(int l, int r) {
			int lTop = l / bucket;
			int rTop = (r - 1) / bucket;
			for (int i = lTop;i < rTop;++ i) lazy(i);
			return Arrays.copyOfRange(bottom, l, r);
		}

		/**
		 * p番目の要素に作用する関数を取得し、その後単位元に差し替えます。
		 * @param p 取得する関数の位置
		 * @return 作用する関数
		 */
		public int poll(int p) {
			lazy(p / bucket);
			int ret = bottom[p];
			bottom[p] = composition.identityAsInt();
			return ret;
		}

		/**
		 * 区間[l, r)に作用する関数を取得し、その後単位元に差し替えます。
		 * @param l 区間の左端(これを含まない)
		 * @param r 区間の右端(これを含む)
		 * @return 作用する関数
		 */
		public int[] poll(int l, int r) {
			int lTop = l / bucket;
			int rTop = (r - 1) / bucket;
			for (int i = lTop;i < rTop;++ i) lazy(i);
			int[] ret = Arrays.copyOfRange(bottom, l, r);
			Arrays.fill(bottom, l, r, composition.identityAsInt());
			return ret;
		}

		/**
		 * 区間[l, r)に順に処理を適用します。
		 * @param l 区間の左端(これを含まない)
		 * @param r 区間の右端(これを含む)
		 * @param action 各要素に対して実行されるアクション
		 */
		public void foreach(int l, int r, IntIndexableConsumer action) {
			int lTop = l / bucket;
			int rTop = (r - 1) / bucket;
			for (int i = lTop;i < rTop;++ i) lazy(i);
			for (int i = l;i < r;++ i) action.acceptAsInt(i, bottom[i]);
		}
	}

	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 IntMonoid {
	static final int FALSE = 0;
	static final int TRUE = 1;
	static final int UNIT = 2;
	static final int NOT = 3;

	@Override
	public int applyAsInt(int after, int before) {
		switch(after) {
			case FALSE:
			case TRUE:
				return after;
			case UNIT:
				return before;
			case NOT:
				return before ^ 1;
		}
		throw new AssertionError();
	}

	@Override
	public int identityAsInt() {
		return UNIT;
	}

	static boolean apply(int operator, boolean argument) {
		switch(operator) {
			case FALSE: return false;
			case TRUE: return true;
			case UNIT: return argument;
			case NOT: return !argument;
		}
		throw new AssertionError();
	}
}

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 IntMonoid extends Monoid<Integer>, IntAssociative, IntUnital {
	@Override
	public default Integer apply(Integer t, Integer u) {
		return applyAsInt(t, u);
	}
	@Override
	public default Integer hyper(Integer element, int repeat) {
		return hyperAsInt(element, repeat);
	}
	@Override
	public default Integer hyper(Integer element, long repeat) {
		return hyperAsInt(element, repeat);
	}
	@Override
	public default int hyperAsInt(int element, int repeat) {
		if (repeat < 0) throw new IllegalArgumentException("undefined operation");
		int ret = identityAsInt();
		for (int mul = element;repeat > 0;repeat >>= 1, mul = applyAsInt(mul, mul)) if ((repeat & 1) != 0) ret = applyAsInt(ret, mul);
		return ret;
	}
	@Override
	public default int hyperAsInt(int element, long repeat) {
		if (repeat < 0) throw new IllegalArgumentException("undefined operation");
		int ret = identityAsInt();
		for (int mul = element;repeat > 0;repeat >>= 1, mul = applyAsInt(mul, mul)) if ((repeat & 1) != 0) ret = applyAsInt(ret, mul);
		return ret;
	}
}

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 IntAssociative extends Associative<Integer>, IntMagma{
	@Override
	public default Integer apply(Integer t, Integer u) {
		return applyAsInt(t, u);
	}
	@Override
	public default Integer hyper(Integer element, int repeat) {
		return hyperAsInt(element, repeat);
	}
	@Override
	public default Integer hyper(Integer element, long repeat) {
		return hyperAsInt(element, repeat);
	}
	public default int hyperAsInt(int element, int repeat) {
		if (repeat < 1) throw new IllegalArgumentException("undefined operation");
		int ret = element;
		-- repeat;
		for (int mul = element;repeat > 0;repeat >>= 1, mul = applyAsInt(mul, mul)) if ((repeat & 1) != 0) ret = applyAsInt(ret, mul);
		return ret;
	}
	public default int hyperAsInt(int element, long repeat) {
		if (repeat < 1) throw new IllegalArgumentException("undefined operation");
		int ret = element;
		-- repeat;
		for (int mul = element;repeat > 0;repeat >>= 1, mul = applyAsInt(mul, mul)) if ((repeat & 1) != 0) ret = applyAsInt(ret, mul);
		return ret;
	}
}

interface IntUnital extends Unital<Integer>, IntMagma {
	@Override
	public default Integer apply(Integer t, Integer u) {
		return applyAsInt(t, u);
	}

	@Override
	public default Integer identity() {
		return identityAsInt();
	}

	public int identityAsInt();
}

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 IntMagma extends Magma<Integer>, java.util.function.IntBinaryOperator {
	@Override
	public default EndoMorphism<Integer> partial(Integer bind) {
		return partialAsInt(bind);
	}

	public default IntEndoMorphism partialAsInt(int bind) {
		return t -> applyAsInt(bind, t);
	}
}


interface Magma<T> extends java.util.function.BinaryOperator<T>{
	public default EndoMorphism<T> partial(T bind) {
		return t -> apply(bind, t);
	}
}


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 IntEndoMorphism extends IntMorphism, EndoMorphism<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);
	}

	public default IntEndoMorphism andThen(IntEndoMorphism after) {
		return s -> after.applyAsInt(applyAsInt(s));
	}

	public default IntEndoMorphism compose(IntEndoMorphism before) {
		return s -> applyAsInt(before.applyAsInt(s));
	}

	public static IntEndoMorphism identity() {
		return t -> t;
	}

	public static Monoid<IntEndoMorphism> composition() {
		return new Monoid<IntEndoMorphism>() {
			@Override
			public IntEndoMorphism apply(IntEndoMorphism t, IntEndoMorphism u) {
				return u.andThen(t);
			}

			@Override
			public IntEndoMorphism identity() {
				return IntEndoMorphism.identity();
			}
		};
	}
}


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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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);
	}
}
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