Problem:
Score : 200 points

Problem Statement

We have a permutation p = {p_1,\ p_2,\ ...,\ p_n} of {1,\ 2,\ ...,\ n}.

Print the number of elements p_i (1 < i < n) that satisfy the following condition:

p_i is the second smallest number among the three numbers p_{i - 1}, p_i, and p_{i + 1}.

Constraints

All values in input are integers.

3 \leq n \leq 20

p is a permutation of {1,\ 2,\ ...,\ n}.

Input

Input is given from Standard Input in the following format:

n
p_1 p_2 ... p_n

Output

Print the number of elements p_i (1 < i < n) that satisfy the condition.

Sample Input 1

5
1 3 5 4 2

Sample Output 1

2

p_2 = 3 is the second smallest number among p_1 = 1, p_2 = 3, and p_3 = 5. Also, p_4 = 4 is the second smallest number among p_3 = 5, p_4 = 4, and p_5 = 2. These two elements satisfy the condition.

Sample Input 2

9
9 6 3 2 5 8 7 4 1

Sample Output 2

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	private static void solve() {
		int n = ni();
		int[] as = nis(n);
		int c = 0;
		for (int i = 1; i < n - 1; i++) {
			int a1 = as[i - 1];
			int a2 = as[i];
			int a3 = as[i + 1];
			if (min(min(a1, a2), a3) != a2 && max(max(a1, a2), a3) != a2)
				c++;
		}
		out(c);
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static <A extends Comparable<? super A>> A min(A a, A b) {
		return a.compareTo(b) < 0 ? a : b;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static <A extends Comparable<? super A>> A max(A a, A b) {
		return a.compareTo(b) > 0 ? a : b;
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static long clamp(long a, long min, long max) {
		return a < min ? min : a > max ? max : a;
	}

	static int abs(int a) {
		return a < 0 ? -a : a;
	}

	static long abs(long a) {
		return a < 0 ? -a : a;
	}

	static <A extends Comparable<? super A>> A clamp(A a, A min, A max) {
		return a.compareTo(min) < 0 ? min : a.compareTo(max) > 0 ? max : a;
	}

	static void out(String val) {
		IO.out(val);
	}

	static void out(Object val) {
		IO.out(String.valueOf(val));
	}

	static void out(int val) {
		IO.out(String.valueOf(val));
	}

	static void out(long val) {
		IO.out(String.valueOf(val));
	}

	static void out(char val) {
		IO.out(String.valueOf(val));
	}

	static void out(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
	}

	static void out(boolean val) {
		IO.out(val ? "true" : "false");
	}

	static void kil(String val) {
		IO.out(val);
		IO.flush();
		System.exit(0);
	}

	static void kil(Object val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(int val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(long val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(char val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(boolean val) {
		IO.out(val ? "true" : "false");
		IO.flush();
		System.exit(0);
	}

	static String ns() {
		return IO.next();
	}

	static int ni() {
		return IO.nextInt();
	}

	static long nl() {
		return IO.nextLong();
	}

	static double nd() {
		return IO.nextDouble();
	}

	static char nc() {
		return IO.nextChar();
	}

	static String[] nss(int n) {
		String[] as = new String[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.next();
		}
		return as;
	}

	static int[] nis(int n) {
		int[] as = new int[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextInt();
		}
		return as;
	}

	static long[] nls(int n) {
		long[] as = new long[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextLong();
		}
		return as;
	}

	static double[] nds(int n) {
		double[] as = new double[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextDouble();
		}
		return as;
	}

	static char[] ncs(int n) {
		char[] as = new char[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextChar();
		}
		return as;
	}

	static String[][] nss2(int n, int m) {
		String[][] as = new String[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.next();
			}
		}
		return as;
	}

	static int[][] nis2(int n, int m) {
		int[][] as = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextInt();
			}
		}
		return as;
	}

	static long[][] nls2(int n, int m) {
		long[][] as = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextLong();
			}
		}
		return as;
	}

	static double[][] nds2(int n, int m) {
		double[][] as = new double[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextDouble();
			}
		}
		return as;
	}

	static char[][] ncs2(int n, int m) {
		char[][] as = new char[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextChar();
			}
		}
		return as;
	}

	static int parseInt(String val) {
		return Integer.parseInt(val);
	}

	static long parseLong(String val) {
		return Long.parseLong(val);
	}

	public static void main(String[] args) {
		try {
			solve();
			IO.flush();
		} catch (NumberFormatException e) {
			e.printStackTrace();
		} catch (OutOfMemoryError e) {
			e.printStackTrace(); // this will be detected as RE
		}
	}
}

final class IO {
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out, false);
	private static final byte[] buffer = new byte[1024];
	private static int ptr = 0;
	private static int len = 0;

	private static boolean hasNextByte() {
		if (ptr < len)
			return true;
		ptr = 0;
		try {
			len = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		return len > 0;
	}

	private static int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	static boolean hasNext() {
		byte c;
		while (hasNextByte() && ((c = buffer[ptr]) < '!' || c > '~'))
			ptr++;
		return hasNextByte();
	}

	static String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b >= '!' && b <= '~') {
			sb.append((char) b);
			b = readByte();
		}
		return sb.toString();
	}

	static char nextChar() {
		if (!hasNext())
			throw new NoSuchElementException();
		return (char) readByte();
	}

	static long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static int nextInt() {
		if (!hasNext())
			throw new NoSuchElementException();
		int n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static double nextDouble() {
		return Double.parseDouble(next());
	}

	static void out(String val) {
		out.println(val);
	}

	static void flush() {
		out.flush();
	}
}

// TODO: paste library here

class UP<A, B> { // Unordered Pair
	A a;
	B b;

	UP(A a, B b) {
		this.a = a;
		this.b = b;
	}

	static <A, B> UP<A, B> make(A a, B b) {
		return new UP<A, B>(a, b);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UP))
			return false;
		UP<?, ?> p = (UP<?, ?>) o;
		boolean aok = a == null ? p.a == null : a.equals(p.a);
		boolean bok = b == null ? p.b == null : b.equals(p.b);
		return aok && bok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ")";
	}
}

class P<A extends Comparable<? super A>, B extends Comparable<? super B>> extends UP<A, B> implements
		Comparable<P<A, B>> { // Pair
	P(A a, B b) {
		super(a, b);
	}

	static <A extends Comparable<? super A>, B extends Comparable<? super B>> P<A, B> make(A a, B b) {
		return new P<A, B>(a, b);
	}

	public int compareTo(P<A, B> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		return sa != 0 ? sa : sb;
	}
}

class PI implements Comparable<PI> { // Pair int
	int a;
	int b;

	PI(int a, int b) {
		this.a = a;
		this.b = b;
	}

	static PI make(int a, int b) {
		return new PI(a, b);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof PI))
			return false;
		PI p = (PI) o;
		return a == p.a && b == p.b;
	}

	public int compareTo(PI o) {
		int sa = a - o.a;
		int sb = b - o.b;
		return sa > 0 ? 1 : sa < 0 ? -1 : sb > 0 ? 1 : sb < 0 ? -1 : 0;
	}

	public String toString() {
		return "(" + a + ", " + b + ")";
	}
}

class PL implements Comparable<PL> { // Pair long
	long a;
	long b;

	PL(long a, long b) {
		this.a = a;
		this.b = b;
	}

	static PL make(long a, long b) {
		return new PL(a, b);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof PL))
			return false;
		PL p = (PL) o;
		return a == p.a && b == p.b;
	}

	public int compareTo(PL o) {
		long sa = a - o.a;
		long sb = b - o.b;
		return sa > 0 ? 1 : sa < 0 ? -1 : sb > 0 ? 1 : sb < 0 ? -1 : 0;
	}

	public String toString() {
		return "(" + a + ", " + b + ")";
	}
}

class UT<A, B, C> { // Unordered Tuple
	A a;
	B b;
	C c;

	UT(A a, B b, C c) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static <A, B, C> UT<A, B, C> make(A a, B b, C c) {
		return new UT<A, B, C>(a, b, c);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UT))
			return false;
		UT<?, ?, ?> t = (UT<?, ?, ?>) o;
		boolean aok = a == null ? t.a == null : a.equals(t.a);
		boolean bok = b == null ? t.b == null : b.equals(t.b);
		boolean cok = c == null ? t.c == null : c.equals(t.c);
		return aok && bok && cok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ", " + c.toString() + ")";
	}
}

class T<A extends Comparable<? super A>, B extends Comparable<? super B>, C extends Comparable<? super C>> extends
		UT<A, B, C> implements Comparable<T<A, B, C>> { // Tuple
	T(A a, B b, C c) {
		super(a, b, c);
	}

	static <A extends Comparable<? super A>, B extends Comparable<? super B>, C extends Comparable<? super C>> T<A, B, C> make(
			A a, B b, C c) {
		return new T<A, B, C>(a, b, c);
	}

	public int compareTo(T<A, B, C> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		int sc = c.compareTo(o.c);
		return sa != 0 ? sa : sb != 0 ? sb : sc;
	}
}

class TI implements Comparable<TI> { // Tuple int
	int a;
	int b;
	int c;

	TI(int a, int b, int c) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static TI make(int a, int b, int c) {
		return new TI(a, b, c);
	}

	TL toLong() {
		return TL.make(a, b, c);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof TI))
			return false;
		TI t = (TI) o;
		return a == t.a && b == t.b && c == t.c;
	}

	public int compareTo(TI o) {
		int sa = a - o.a;
		int sb = b - o.b;
		int sc = c - o.c;
		return sa > 0 ? 1 : sa < 0 ? -1 : sb > 0 ? 1 : sb < 0 ? -1 : sc > 0 ? 1 : sc < 0 ? -1 : 0;
	}

	public String toString() {
		return "(" + a + ", " + b + ", " + c + ")";
	}
}

class TL implements Comparable<TL> { // Tuple long
	long a;
	long b;
	long c;

	TL(long a, long b, long c) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static TL make(long a, long b, long c) {
		return new TL(a, b, c);
	}

	TI toInt() {
		return TI.make((int) a, (int) b, (int) c);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof TL))
			return false;
		TL t = (TL) o;
		return a == t.a && b == t.b && c == t.c;
	}

	public int compareTo(TL o) {
		long sa = a - o.a;
		long sb = b - o.b;
		long sc = c - o.c;
		return sa > 0 ? 1 : sa < 0 ? -1 : sb > 0 ? 1 : sb < 0 ? -1 : sc > 0 ? 1 : sc < 0 ? -1 : 0;
	}

	public String toString() {
		return "(" + a + ", " + b + ", " + c + ")";
	}
}

final class U { // Utilities
	private U() {
	}

	static <A> ArrayList<A> make(int n, F.IX<A> maker) {
		ArrayList<A> res = new ArrayList<A>();
		for (int i = 0; i < n; i++)
			res.add(maker.f(i));
		return res;
	}

	static boolean[] makeB(int n, F.IB maker) {
		boolean[] res = new boolean[n];
		for (int i = 0; i < n; i++)
			res[i] = maker.f(i);
		return res;
	}

	static int[] makeI(int n, F.II maker) {
		int[] res = new int[n];
		for (int i = 0; i < n; i++)
			res[i] = maker.f(i);
		return res;
	}

	static long[] makeL(int n, F.IL maker) {
		long[] res = new long[n];
		for (int i = 0; i < n; i++)
			res[i] = maker.f(i);
		return res;
	}

	static <A> A[] makeX(int n, F.IX<A> maker, A[] as) {
		A[] res = Arrays.copyOf(as, n);
		for (int i = 0; i < n; i++)
			res[i] = maker.f(i);
		return res;
	}

	static <A> ArrayList<A> filter(ArrayList<A> as, F.XB<A> pred) {
		ArrayList<A> res = new ArrayList<A>();
		for (A a : as)
			if (pred.f(a))
				res.add(a);
		return res;
	}

	static <A> int count(ArrayList<A> as, F.XB<A> pred) {
		int res = 0;
		for (A a : as)
			if (pred.f(a))
				res++;
		return res;
	}

	static <A> ArrayList<A> concat(ArrayList<A> as, ArrayList<A> bs) {
		ArrayList<A> res = new ArrayList<A>();
		res.addAll(as);
		res.addAll(bs);
		return res;
	}

	static <A> boolean any(ArrayList<A> as, F.XB<A> pred) {
		for (A a : as)
			if (pred.f(a))
				return true;
		return false;
	}

	static <A> boolean all(ArrayList<A> as, F.XB<A> pred) {
		for (A a : as)
			if (!pred.f(a))
				return false;
		return true;
	}

	static <A> ArrayList<A> flatten(ArrayList<ArrayList<A>> ass) {
		ArrayList<A> res = new ArrayList<A>();
		for (ArrayList<A> as : ass)
			res.addAll(as);
		return res;
	}

	static <A, B> B foldl(ArrayList<A> as, F.XXX<B, A, B> f, B e) {
		B res = e;
		for (A a : as)
			res = f.f(res, a);
		return res;
	}

	static <A, B> B foldr(ArrayList<A> as, F.XXX<A, B, B> f, B e) {
		B res = e;
		for (int i = as.size() - 1; i >= 0; i--)
			res = f.f(as.get(i), res);
		return res;
	}

	static <A> ArrayList<A> reverse(ArrayList<A> as) {
		int size = as.size();
		return make(size, i -> as.get(size - 1 - i));
	}

	static boolean[] reverse(boolean[] as) {
		int size = as.length;
		return makeB(size, i -> as[size - 1 - i]);
	}

	static int[] reverse(int[] as) {
		int size = as.length;
		return makeI(size, i -> as[size - 1 - i]);
	}

	static long[] reverse(long[] as) {
		int size = as.length;
		return makeL(size, i -> as[size - 1 - i]);
	}

	static <A> A[] reverse(A[] as) {
		int size = as.length;
		return makeX(size, i -> as[size - 1 - i], as);
	}

	static <A extends Comparable<? super A>> UP<TreeMap<A, Integer>, ArrayList<A>> compress(ArrayList<A> as) {
		TreeSet<A> set = new TreeSet<A>(as);
		TreeMap<A, Integer> map = new TreeMap<A, Integer>();
		ArrayList<A> imap = new ArrayList<A>();
		int i = 0;
		for (A a : set) {
			map.put(a, i++);
			imap.add(a);
		}
		return UP.make(map, imap);
	}

	static <A, B> ArrayList<B> map(ArrayList<A> as, F.XX<A, B> f) {
		return make(as.size(), (i) -> f.f(as.get(i)));
	}

	static <A, B> ArrayList<B> mapi(ArrayList<A> as, F.XIX<A, B> f) {
		return make(as.size(), (i) -> f.f(as.get(i), i));
	}

	static <A, B> ArrayList<UP<A, B>> zip(ArrayList<A> as, ArrayList<B> bs) {
		return make(min(as.size(), bs.size()), (i) -> UP.make(as.get(i), bs.get(i)));
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static <A extends Comparable<? super A>> A min(A a, A b) {
		return a.compareTo(b) < 0 ? a : b;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static <A extends Comparable<? super A>> A max(A a, A b) {
		return a.compareTo(b) > 0 ? a : b;
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static long clamp(long a, long min, long max) {
		return a < min ? min : a > max ? max : a;
	}

	static <A extends Comparable<? super A>> A clamp(A a, A min, A max) {
		return a.compareTo(min) < 0 ? min : a.compareTo(max) > 0 ? max : a;
	}

	static int abs(int a) {
		return a < 0 ? -a : a;
	}

	static long abs(long a) {
		return a < 0 ? -a : a;
	}

	static void forEachBitPerm(int n, int k, F.IV f) {
		for (int i = (1 << k) - 1; i < 1 << n;) {
			f.f(i);
			int t = (i | i - 1) + 1;
			i = t | ((t & -t) / (i & -i) >> 1) - 1;
		}
	}

	static int nextBitPerm(int a) {
		int t = (a | a - 1) + 1;
		return t | ((t & -t) / (a & -a) >> 1) - 1;
	}

	static void mebius(int n, F.IIV f) { // s, i
		int bit = 1;
		int exp = 0;
		for (int i = 1; i < 1 << n; i++) {
			f.f(i ^ bit, exp);
			if ((i & i + 1) == 0) {
				bit <<= 1;
				exp++;
			}
		}
	}

	static void zeta(int n, F.IIV f) { // s, i
		int m = (1 << n) - 1;
		int bit = 1;
		int exp = 0;
		for (int i = (1 << n) - 2; i >= 0; i--) {
			f.f(i ^ bit, exp);
			if ((~i & ~i + 1 & m) == 0) {
				bit <<= 1;
				exp++;
			}
		}
	}

	static <A> ArrayList<A> toAL(A[] as) {
		return make(as.length, i -> as[i]);
	}

	static <A> A[] doubleSize(A[] as) {
		return Arrays.copyOf(as, as.length << 1);
	}

	static long searchL(long ng, long ok, F.LB isOk) {
		while (ng - ok > 1 || ok - ng > 1) {
			long mid = ng + ok >> 1;
			if (isOk.f(mid))
				ok = mid;
			else
				ng = mid;
		}
		return ok;
	}

	static int searchI(int ng, int ok, F.IB isOk) {
		return (int) searchL((long) ng, (long) ok, (mid) -> isOk.f((int) mid));
	}
}

final class F { // Functions
	private F() {
	}

	interface VV {
		void f();
	}

	interface BV {
		void f(boolean a);
	}

	interface BXV<A> {
		void f(boolean a, A b);
	}

	interface BXXV<A, B> {
		void f(boolean a, A b, B c);
	}

	interface BXXXV<A, B, C> {
		void f(boolean a, A b, B c, C d);
	}

	interface XBV<A> {
		void f(A a, boolean b);
	}

	interface XXBV<A, B> {
		void f(A a, B b, boolean c);
	}

	interface XXXBV<A, B, C> {
		void f(A a, B b, C c, boolean d);
	}

	interface IV {
		void f(int a);
	}

	interface IXV<A> {
		void f(int a, A b);
	}

	interface IXXV<A, B> {
		void f(int a, A b, B c);
	}

	interface IXXXV<A, B, C> {
		void f(int a, A b, B c, C d);
	}

	interface XIV<A> {
		void f(A a, int b);
	}

	interface XXIV<A, B> {
		void f(A a, B b, int c);
	}

	interface XXXIV<A, B, C> {
		void f(A a, B b, C c, int d);
	}

	interface LV {
		void f(long a);
	}

	interface LXV<A> {
		void f(long a, A b);
	}

	interface LXXV<A, B> {
		void f(long a, A b, B c);
	}

	interface LXXXV<A, B, C> {
		void f(long a, A b, B c, C d);
	}

	interface XLV<A> {
		void f(A a, long b);
	}

	interface XXLV<A, B> {
		void f(A a, B b, long c);
	}

	interface XXXLV<A, B, C> {
		void f(A a, B b, C c, long d);
	}

	interface DV {
		void f(double a);
	}

	interface DXV<A> {
		void f(double a, A b);
	}

	interface DXXV<A, B> {
		void f(double a, A b, B c);
	}

	interface DXXXV<A, B, C> {
		void f(double a, A b, B c, C d);
	}

	interface XDV<A> {
		void f(A a, double b);
	}

	interface XXDV<A, B> {
		void f(A a, B b, double c);
	}

	interface XXXDV<A, B, C> {
		void f(A a, B b, C c, double d);
	}

	interface XV<A> {
		void f(A a);
	}

	interface XXV<A, B> {
		void f(A a, B b);
	}

	interface XXXV<A, B, C> {
		void f(A a, B b, C c);
	}

	interface XXXXV<A, B, C, D> {
		void f(A a, B b, C c, D d);
	}

	interface BBV {
		void f(boolean a, boolean b);
	}

	interface BIV {
		void f(boolean a, int b);
	}

	interface BLV {
		void f(boolean a, long b);
	}

	interface BDV {
		void f(boolean a, double b);
	}

	interface IBV {
		void f(int a, boolean b);
	}

	interface IIV {
		void f(int a, int b);
	}

	interface ILV {
		void f(int a, long b);
	}

	interface IDV {
		void f(int a, double b);
	}

	interface LBV {
		void f(long a, boolean b);
	}

	interface LIV {
		void f(long a, int b);
	}

	interface LLV {
		void f(long a, long b);
	}

	interface LDV {
		void f(long a, double b);
	}

	interface DBV {
		void f(double a, boolean b);
	}

	interface DIV {
		void f(double a, int b);
	}

	interface DLV {
		void f(double a, long b);
	}

	interface DDV {
		void f(double a, double b);
	}

	interface VB {
		boolean f();
	}

	interface BB {
		boolean f(boolean a);
	}

	interface BXB<A> {
		boolean f(boolean a, A b);
	}

	interface BXXB<A, B> {
		boolean f(boolean a, A b, B c);
	}

	interface BXXXB<A, B, C> {
		boolean f(boolean a, A b, B c, C d);
	}

	interface XBB<A> {
		boolean f(A a, boolean b);
	}

	interface XXBB<A, B> {
		boolean f(A a, B b, boolean c);
	}

	interface XXXBB<A, B, C> {
		boolean f(A a, B b, C c, boolean d);
	}

	interface IB {
		boolean f(int a);
	}

	interface IXB<A> {
		boolean f(int a, A b);
	}

	interface IXXB<A, B> {
		boolean f(int a, A b, B c);
	}

	interface IXXXB<A, B, C> {
		boolean f(int a, A b, B c, C d);
	}

	interface XIB<A> {
		boolean f(A a, int b);
	}

	interface XXIB<A, B> {
		boolean f(A a, B b, int c);
	}

	interface XXXIB<A, B, C> {
		boolean f(A a, B b, C c, int d);
	}

	interface LB {
		boolean f(long a);
	}

	interface LXB<A> {
		boolean f(long a, A b);
	}

	interface LXXB<A, B> {
		boolean f(long a, A b, B c);
	}

	interface LXXXB<A, B, C> {
		boolean f(long a, A b, B c, C d);
	}

	interface XLB<A> {
		boolean f(A a, long b);
	}

	interface XXLB<A, B> {
		boolean f(A a, B b, long c);
	}

	interface XXXLB<A, B, C> {
		boolean f(A a, B b, C c, long d);
	}

	interface DB {
		boolean f(double a);
	}

	interface DXB<A> {
		boolean f(double a, A b);
	}

	interface DXXB<A, B> {
		boolean f(double a, A b, B c);
	}

	interface DXXXB<A, B, C> {
		boolean f(double a, A b, B c, C d);
	}

	interface XDB<A> {
		boolean f(A a, double b);
	}

	interface XXDB<A, B> {
		boolean f(A a, B b, double c);
	}

	interface XXXDB<A, B, C> {
		boolean f(A a, B b, C c, double d);
	}

	interface XB<A> {
		boolean f(A a);
	}

	interface XXB<A, B> {
		boolean f(A a, B b);
	}

	interface XXXB<A, B, C> {
		boolean f(A a, B b, C c);
	}

	interface XXXXB<A, B, C, D> {
		boolean f(A a, B b, C c, D d);
	}

	interface BBB {
		boolean f(boolean a, boolean b);
	}

	interface BIB {
		boolean f(boolean a, int b);
	}

	interface BLB {
		boolean f(boolean a, long b);
	}

	interface BDB {
		boolean f(boolean a, double b);
	}

	interface IBB {
		boolean f(int a, boolean b);
	}

	interface IIB {
		boolean f(int a, int b);
	}

	interface ILB {
		boolean f(int a, long b);
	}

	interface IDB {
		boolean f(int a, double b);
	}

	interface LBB {
		boolean f(long a, boolean b);
	}

	interface LIB {
		boolean f(long a, int b);
	}

	interface LLB {
		boolean f(long a, long b);
	}

	interface LDB {
		boolean f(long a, double b);
	}

	interface DBB {
		boolean f(double a, boolean b);
	}

	interface DIB {
		boolean f(double a, int b);
	}

	interface DLB {
		boolean f(double a, long b);
	}

	interface DDB {
		boolean f(double a, double b);
	}

	interface VI {
		int f();
	}

	interface BI {
		int f(boolean a);
	}

	interface BXI<A> {
		int f(boolean a, A b);
	}

	interface BXXI<A, B> {
		int f(boolean a, A b, B c);
	}

	interface BXXXI<A, B, C> {
		int f(boolean a, A b, B c, C d);
	}

	interface XBI<A> {
		int f(A a, boolean b);
	}

	interface XXBI<A, B> {
		int f(A a, B b, boolean c);
	}

	interface XXXBI<A, B, C> {
		int f(A a, B b, C c, boolean d);
	}

	interface II {
		int f(int a);
	}

	interface IXI<A> {
		int f(int a, A b);
	}

	interface IXXI<A, B> {
		int f(int a, A b, B c);
	}

	interface IXXXI<A, B, C> {
		int f(int a, A b, B c, C d);
	}

	interface XII<A> {
		int f(A a, int b);
	}

	interface XXII<A, B> {
		int f(A a, B b, int c);
	}

	interface XXXII<A, B, C> {
		int f(A a, B b, C c, int d);
	}

	interface LI {
		int f(long a);
	}

	interface LXI<A> {
		int f(long a, A b);
	}

	interface LXXI<A, B> {
		int f(long a, A b, B c);
	}

	interface LXXXI<A, B, C> {
		int f(long a, A b, B c, C d);
	}

	interface XLI<A> {
		int f(A a, long b);
	}

	interface XXLI<A, B> {
		int f(A a, B b, long c);
	}

	interface XXXLI<A, B, C> {
		int f(A a, B b, C c, long d);
	}

	interface DI {
		int f(double a);
	}

	interface DXI<A> {
		int f(double a, A b);
	}

	interface DXXI<A, B> {
		int f(double a, A b, B c);
	}

	interface DXXXI<A, B, C> {
		int f(double a, A b, B c, C d);
	}

	interface XDI<A> {
		int f(A a, double b);
	}

	interface XXDI<A, B> {
		int f(A a, B b, double c);
	}

	interface XXXDI<A, B, C> {
		int f(A a, B b, C c, double d);
	}

	interface XI<A> {
		int f(A a);
	}

	interface XXI<A, B> {
		int f(A a, B b);
	}

	interface XXXI<A, B, C> {
		int f(A a, B b, C c);
	}

	interface XXXXI<A, B, C, D> {
		int f(A a, B b, C c, D d);
	}

	interface BBI {
		int f(boolean a, boolean b);
	}

	interface BII {
		int f(boolean a, int b);
	}

	interface BLI {
		int f(boolean a, long b);
	}

	interface BDI {
		int f(boolean a, double b);
	}

	interface IBI {
		int f(int a, boolean b);
	}

	interface III {
		int f(int a, int b);
	}

	interface ILI {
		int f(int a, long b);
	}

	interface IDI {
		int f(int a, double b);
	}

	interface LBI {
		int f(long a, boolean b);
	}

	interface LII {
		int f(long a, int b);
	}

	interface LLI {
		int f(long a, long b);
	}

	interface LDI {
		int f(long a, double b);
	}

	interface DBI {
		int f(double a, boolean b);
	}

	interface DII {
		int f(double a, int b);
	}

	interface DLI {
		int f(double a, long b);
	}

	interface DDI {
		int f(double a, double b);
	}

	interface VL {
		long f();
	}

	interface BL {
		long f(boolean a);
	}

	interface BXL<A> {
		long f(boolean a, A b);
	}

	interface BXXL<A, B> {
		long f(boolean a, A b, B c);
	}

	interface BXXXL<A, B, C> {
		long f(boolean a, A b, B c, C d);
	}

	interface XBL<A> {
		long f(A a, boolean b);
	}

	interface XXBL<A, B> {
		long f(A a, B b, boolean c);
	}

	interface XXXBL<A, B, C> {
		long f(A a, B b, C c, boolean d);
	}

	interface IL {
		long f(int a);
	}

	interface IXL<A> {
		long f(int a, A b);
	}

	interface IXXL<A, B> {
		long f(int a, A b, B c);
	}

	interface IXXXL<A, B, C> {
		long f(int a, A b, B c, C d);
	}

	interface XIL<A> {
		long f(A a, int b);
	}

	interface XXIL<A, B> {
		long f(A a, B b, int c);
	}

	interface XXXIL<A, B, C> {
		long f(A a, B b, C c, int d);
	}

	interface LL {
		long f(long a);
	}

	interface LXL<A> {
		long f(long a, A b);
	}

	interface LXXL<A, B> {
		long f(long a, A b, B c);
	}

	interface LXXXL<A, B, C> {
		long f(long a, A b, B c, C d);
	}

	interface XLL<A> {
		long f(A a, long b);
	}

	interface XXLL<A, B> {
		long f(A a, B b, long c);
	}

	interface XXXLL<A, B, C> {
		long f(A a, B b, C c, long d);
	}

	interface DL {
		long f(double a);
	}

	interface DXL<A> {
		long f(double a, A b);
	}

	interface DXXL<A, B> {
		long f(double a, A b, B c);
	}

	interface DXXXL<A, B, C> {
		long f(double a, A b, B c, C d);
	}

	interface XDL<A> {
		long f(A a, double b);
	}

	interface XXDL<A, B> {
		long f(A a, B b, double c);
	}

	interface XXXDL<A, B, C> {
		long f(A a, B b, C c, double d);
	}

	interface XL<A> {
		long f(A a);
	}

	interface XXL<A, B> {
		long f(A a, B b);
	}

	interface XXXL<A, B, C> {
		long f(A a, B b, C c);
	}

	interface XXXXL<A, B, C, D> {
		long f(A a, B b, C c, D d);
	}

	interface BBL {
		long f(boolean a, boolean b);
	}

	interface BIL {
		long f(boolean a, int b);
	}

	interface BLL {
		long f(boolean a, long b);
	}

	interface BDL {
		long f(boolean a, double b);
	}

	interface IBL {
		long f(int a, boolean b);
	}

	interface IIL {
		long f(int a, int b);
	}

	interface ILL {
		long f(int a, long b);
	}

	interface IDL {
		long f(int a, double b);
	}

	interface LBL {
		long f(long a, boolean b);
	}

	interface LIL {
		long f(long a, int b);
	}

	interface LLL {
		long f(long a, long b);
	}

	interface LDL {
		long f(long a, double b);
	}

	interface DBL {
		long f(double a, boolean b);
	}

	interface DIL {
		long f(double a, int b);
	}

	interface DLL {
		long f(double a, long b);
	}

	interface DDL {
		long f(double a, double b);
	}

	interface VD {
		double f();
	}

	interface BD {
		double f(boolean a);
	}

	interface BXD<A> {
		double f(boolean a, A b);
	}

	interface BXXD<A, B> {
		double f(boolean a, A b, B c);
	}

	interface BXXXD<A, B, C> {
		double f(boolean a, A b, B c, C d);
	}

	interface XBD<A> {
		double f(A a, boolean b);
	}

	interface XXBD<A, B> {
		double f(A a, B b, boolean c);
	}

	interface XXXBD<A, B, C> {
		double f(A a, B b, C c, boolean d);
	}

	interface ID {
		double f(int a);
	}

	interface IXD<A> {
		double f(int a, A b);
	}

	interface IXXD<A, B> {
		double f(int a, A b, B c);
	}

	interface IXXXD<A, B, C> {
		double f(int a, A b, B c, C d);
	}

	interface XID<A> {
		double f(A a, int b);
	}

	interface XXID<A, B> {
		double f(A a, B b, int c);
	}

	interface XXXID<A, B, C> {
		double f(A a, B b, C c, int d);
	}

	interface LD {
		double f(long a);
	}

	interface LXD<A> {
		double f(long a, A b);
	}

	interface LXXD<A, B> {
		double f(long a, A b, B c);
	}

	interface LXXXD<A, B, C> {
		double f(long a, A b, B c, C d);
	}

	interface XLD<A> {
		double f(A a, long b);
	}

	interface XXLD<A, B> {
		double f(A a, B b, long c);
	}

	interface XXXLD<A, B, C> {
		double f(A a, B b, C c, long d);
	}

	interface DD {
		double f(double a);
	}

	interface DXD<A> {
		double f(double a, A b);
	}

	interface DXXD<A, B> {
		double f(double a, A b, B c);
	}

	interface DXXXD<A, B, C> {
		double f(double a, A b, B c, C d);
	}

	interface XDD<A> {
		double f(A a, double b);
	}

	interface XXDD<A, B> {
		double f(A a, B b, double c);
	}

	interface XXXDD<A, B, C> {
		double f(A a, B b, C c, double d);
	}

	interface XD<A> {
		double f(A a);
	}

	interface XXD<A, B> {
		double f(A a, B b);
	}

	interface XXXD<A, B, C> {
		double f(A a, B b, C c);
	}

	interface XXXXD<A, B, C, D> {
		double f(A a, B b, C c, D d);
	}

	interface BBD {
		double f(boolean a, boolean b);
	}

	interface BID {
		double f(boolean a, int b);
	}

	interface BLD {
		double f(boolean a, long b);
	}

	interface BDD {
		double f(boolean a, double b);
	}

	interface IBD {
		double f(int a, boolean b);
	}

	interface IID {
		double f(int a, int b);
	}

	interface ILD {
		double f(int a, long b);
	}

	interface IDD {
		double f(int a, double b);
	}

	interface LBD {
		double f(long a, boolean b);
	}

	interface LID {
		double f(long a, int b);
	}

	interface LLD {
		double f(long a, long b);
	}

	interface LDD {
		double f(long a, double b);
	}

	interface DBD {
		double f(double a, boolean b);
	}

	interface DID {
		double f(double a, int b);
	}

	interface DLD {
		double f(double a, long b);
	}

	interface DDD {
		double f(double a, double b);
	}

	interface VX<A> {
		A f();
	}

	interface BX<A> {
		A f(boolean a);
	}

	interface BXX<A, B> {
		B f(boolean a, A b);
	}

	interface BXXX<A, B, C> {
		C f(boolean a, A b, B c);
	}

	interface BXXXX<A, B, C, D> {
		D f(boolean a, A b, B c, C d);
	}

	interface XBX<A, B> {
		B f(A a, boolean b);
	}

	interface XXBX<A, B, C> {
		C f(A a, B b, boolean c);
	}

	interface XXXBX<A, B, C, D> {
		D f(A a, B b, C c, boolean d);
	}

	interface IX<A> {
		A f(int a);
	}

	interface IXX<A, B> {
		B f(int a, A b);
	}

	interface IXXX<A, B, C> {
		C f(int a, A b, B c);
	}

	interface IXXXX<A, B, C, D> {
		D f(int a, A b, B c, C d);
	}

	interface XIX<A, B> {
		B f(A a, int b);
	}

	interface XXIX<A, B, C> {
		C f(A a, B b, int c);
	}

	interface XXXIX<A, B, C, D> {
		D f(A a, B b, C c, int d);
	}

	interface LX<A> {
		A f(long a);
	}

	interface LXX<A, B> {
		B f(long a, A b);
	}

	interface LXXX<A, B, C> {
		C f(long a, A b, B c);
	}

	interface LXXXX<A, B, C, D> {
		D f(long a, A b, B c, C d);
	}

	interface XLX<A, B> {
		B f(A a, long b);
	}

	interface XXLX<A, B, C> {
		C f(A a, B b, long c);
	}

	interface XXXLX<A, B, C, D> {
		D f(A a, B b, C c, long d);
	}

	interface DX<A> {
		A f(double a);
	}

	interface DXX<A, B> {
		B f(double a, A b);
	}

	interface DXXX<A, B, C> {
		C f(double a, A b, B c);
	}

	interface DXXXX<A, B, C, D> {
		D f(double a, A b, B c, C d);
	}

	interface XDX<A, B> {
		B f(A a, double b);
	}

	interface XXDX<A, B, C> {
		C f(A a, B b, double c);
	}

	interface XXXDX<A, B, C, D> {
		D f(A a, B b, C c, double d);
	}

	interface XX<A, B> {
		B f(A a);
	}

	interface XXX<A, B, C> {
		C f(A a, B b);
	}

	interface XXXX<A, B, C, D> {
		D f(A a, B b, C c);
	}

	interface XXXXX<A, B, C, D, E> {
		E f(A a, B b, C c, D d);
	}

	interface BBX<A> {
		A f(boolean a, boolean b);
	}

	interface BIX<A> {
		A f(boolean a, int b);
	}

	interface BLX<A> {
		A f(boolean a, long b);
	}

	interface BDX<A> {
		A f(boolean a, double b);
	}

	interface IBX<A> {
		A f(int a, boolean b);
	}

	interface IIX<A> {
		A f(int a, int b);
	}

	interface ILX<A> {
		A f(int a, long b);
	}

	interface IDX<A> {
		A f(int a, double b);
	}

	interface LBX<A> {
		A f(long a, boolean b);
	}

	interface LIX<A> {
		A f(long a, int b);
	}

	interface LLX<A> {
		A f(long a, long b);
	}

	interface LDX<A> {
		A f(long a, double b);
	}

	interface DBX<A> {
		A f(double a, boolean b);
	}

	interface DIX<A> {
		A f(double a, int b);
	}

	interface DLX<A> {
		A f(double a, long b);
	}

	interface DDX<A> {
		A f(double a, double b);
	}
}

class SA { // suffix array
	static int[] makeSA(String s) {
		int n = s.length() + 1;
		int[] cs = new int[n];
		cs[n - 1] = 0;
		for (int i = 0; i < n - 1; i++)
			cs[i] = s.charAt(i) + 1;
		ArrayList<Integer> acs = U.make(n, i -> cs[i]);
		TreeMap<Integer, Integer> tm = U.compress(acs).a;
		int k = tm.size();
		for (int i = 0; i < n; i++)
			cs[i] = tm.get(cs[i]);
		return makeSA(cs, n, k);
	}

	static int[] makeLCP(String s, int[] sa) { // lcp(i, i+1)
		int n = sa.length;
		int[] r = new int[n];
		for (int i = 0; i < n; i++)
			r[sa[i]] = i;
		int[] lcp = new int[n];
		int l = 0;
		for (int i = 0; i < n; i++) {
			int idx = r[i];
			if (idx == n - 1) {
				lcp[idx] = -1;
				l = 0;
				continue;
			}
			int p = sa[idx];
			int q = sa[idx + 1];
			if (l > 0)
				l--;
			while (p + l < n - 1 && q + l < n - 1 && s.charAt(p + l) == s.charAt(q + l))
				l++;
			lcp[idx] = l;
		}
		return lcp;
	}

	static F.III lcpQuery(String s) {
		int n = s.length() + 1;
		int[] sa = makeSA(s);
		int[] lcp = makeLCP(s, sa);
		int[] inv = new int[n];
		for (int i = 0; i < n; i++) {
			inv[sa[i]] = i;
		}
		ST<Integer> st = new ST<Integer>(n, (a, b) -> a < b ? a : b, Integer.MAX_VALUE);
		st.init(i -> i < n ? lcp[i] : Integer.MAX_VALUE);
		return (i, j) -> {
			if (i == j)
				return n - 1 - i;
			i = inv[i];
			j = inv[j];
			if (i > j) {
				i ^= j;
				j ^= i;
				i ^= j;
			}
			return st.query(i, j);
		};
	}

	private static int[] makeSA(int[] cs, int n, int k) {
		boolean[] isS = new boolean[n];
		boolean[] isLms = new boolean[n];
		int[] lmss = new int[n];
		int numLmss = 0;
		isS[n - 1] = true;
		for (int i = n - 2; i >= 0; i--)
			isS[i] = cs[i] < cs[i + 1] || cs[i] == cs[i + 1] && isS[i + 1];
		for (int i = 1; i < n; i++)
			if (!isS[i - 1] && isS[i]) {
				lmss[numLmss++] = i;
				isLms[i] = true;
			}
		int[] sa = inducedSort(cs, n, numLmss, k, lmss, isS);
		int[] lmss2 = new int[numLmss];
		numLmss = 0;
		for (int i = 0; i < n; i++)
			if (isLms[sa[i]])
				lmss2[numLmss++] = sa[i];
		int num = 0;
		sa[lmss2[0]] = 0;
		for (int i = 0; i < numLmss - 1; i++) {
			int p = lmss2[i];
			int q = lmss2[i + 1];
			for (int j = 0; j < n; j++) {
				if (cs[p] != cs[q] || isLms[p] != isLms[q]) {
					sa[lmss2[i + 1]] = ++num;
					break;
				} else if (j > 0 && (isLms[p] || isLms[q])) {
					sa[lmss2[i + 1]] = num;
					break;
				}
				p++;
				q++;
			}
		}
		if (num + 1 < numLmss) {
			numLmss = 0;
			for (int i = 0; i < n; i++)
				if (isLms[i])
					lmss2[numLmss++] = sa[i];
			lmss2 = makeSA(lmss2, numLmss, num + 1);
			for (int i = 0; i < numLmss; i++)
				lmss2[i] = lmss[lmss2[i]];
		}
		return inducedSort(cs, n, numLmss, k, lmss2, isS);
	}

	private static int[] inducedSort(int[] cs, int n, int numLmss, int k, int[] lmss, boolean[] isS) {
		int[] sa = new int[n];
		int[] bin = new int[k + 1];
		for (int i = 0; i < n; i++)
			bin[cs[i] + 1]++;
		for (int i = 0; i < k; i++)
			bin[i + 1] += bin[i];
		int[] counts = new int[k];
		for (int i = numLmss - 1; i >= 0; i--) { // put LMS backward
			int c = cs[lmss[i]];
			sa[bin[c + 1] - 1 - counts[c]++] = lmss[i];
		}
		for (int i = 0; i < k; i++)
			counts[i] = 0;
		for (int i = 0; i < n; i++) { // put L forward
			int s = sa[i] - 1;
			if (s < 0 || isS[s])
				continue;
			int c = cs[s];
			sa[bin[c] + counts[c]++] = s;
		}
		for (int i = 0; i < k; i++)
			counts[i] = 0;
		for (int i = n - 1; i >= 0; i--) { // put S backward
			int s = sa[i] - 1;
			if (s < 0 || !isS[s])
				continue;
			int c = cs[s];
			sa[bin[c + 1] - 1 - counts[c]++] = s;
		}
		return sa;
	}
}

class ST<A> { // Segment Tree
	private ArrayList<A> as;
	private int h;
	private int n;
	private F.XXX<A, A, A> merger;
	private A e;

	ST(int num, F.XXX<A, A, A> merger, A e) {
		this.merger = merger;
		this.e = e;
		h = 0;
		while ((1 << h) < num)
			h++;
		n = 1 << h;
		as = U.make(2 * n, i -> e);
	}

	void init(A a) {
		init(i -> a);
	}

	void init(A[] as) {
		init(i -> i < as.length ? as[i] : e);
	}

	void init(F.IX<A> maker) {
		for (int i = 0; i < n; i++)
			as.set(n + i, maker.f(i));
		for (int i = n - 1; i > 0; i--)
			as.set(i, merge(as.get(i << 1), as.get(i << 1 | 1)));
	}

	A get(int i) {
		return query(i, i + 1);
	}

	void set(int i, A a) {
		as.set(i += n, a);
		while ((i >>= 1) > 0)
			as.set(i, merge(as.get(i << 1), as.get(i << 1 | 1)));
	}

	A query(int l, int r) {
		l += n;
		r += n;
		A al = e;
		A ar = e;
		while (l < r) {
			if ((l & 1) != 0)
				al = merge(al, as.get(l++));
			if ((r & 1) != 0)
				ar = merge(as.get(--r), ar);
			l >>= 1;
			r >>= 1;
		}
		return merge(al, ar);
	}

	private A merge(A a, A b) {
		return a == e ? b : b == e ? a : merger.f(a, b);
	}
}