import java.util.*; import java.io.*; public class Main { static StringBuilder sb; static dsu dsu; static long fact[]; static int mod = (int) (1e9 + 7); static void solve() { } public static void main(String[] args) { sb = new StringBuilder(); int test = 1; while (test-- > 0) { solve(); } System.out.println(sb); } /* * fact=new long[(int)1e6+10]; fact[0]=fact[1]=1; for(int i=2;i n) return (long) 0; long res = fact[n] % mod; // System.out.println(res); res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod; res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod; // System.out.println(res); return res; } static long p(long x, long y)// POWER FXN // { if (y == 0) return 1; long res = 1; while (y > 0) { if (y % 2 == 1) { res = (res * x) % mod; y--; } x = (x * x) % mod; y = y / 2; } return res; } //**************END****************** // *************Disjoint set // union*********// static class dsu { int parent[]; dsu(int n) { parent = new int[n]; for (int i = 0; i < n; i++) parent[i] = -1; } int find(int a) { if (parent[a] < 0) return a; else { int x = find(parent[a]); parent[a] = x; return x; } } void merge(int a, int b) { a = find(a); b = find(b); if (a == b) return; parent[b] = a; } } //**************PRIME FACTORIZE **********************************// static TreeMap prime(long n) { TreeMap h = new TreeMap<>(); long num = n; for (int i = 2; i <= Math.sqrt(num); i++) { if (n % i == 0) { int nt = 0; while (n % i == 0) { n = n / i; nt++; } h.put(i, nt); } } if (n != 1) h.put((int) n, 1); return h; } //****CLASS PAIR ************************************************ static class Pair implements Comparable { int x; long y; Pair(int x, long y) { this.x = x; this.y = y; } public int compareTo(Pair o) { return (int) (this.y - o.y); } } //****CLASS PAIR ************************************************** static class InputReader { private InputStream stream; private byte[] buf = new byte[1024]; private int curChar; private int numChars; private SpaceCharFilter filter; public InputReader(InputStream stream) { this.stream = stream; } public int read() { if (numChars == -1) throw new InputMismatchException(); if (curChar >= numChars) { curChar = 0; try { numChars = stream.read(buf); } catch (IOException e) { throw new InputMismatchException(); } if (numChars <= 0) return -1; } return buf[curChar++]; } public int Int() { int c = read(); while (isSpaceChar(c)) c = read(); int sgn = 1; if (c == ''-'') { sgn = -1; c = read(); } int res = 0; do { if (c < ''0'' || c > ''9'') throw new InputMismatchException(); res *= 10; res += c - ''0''; c = read(); } while (!isSpaceChar(c)); return res * sgn; } public String String() { int c = read(); while (isSpaceChar(c)) c = read(); StringBuilder res = new StringBuilder(); do { res.appendCodePoint(c); c = read(); } while (!isSpaceChar(c)); return res.toString(); } public boolean isSpaceChar(int c) { if (filter != null) return filter.isSpaceChar(c); return c == '' '' || c == ''\n'' || c == ''\r'' || c == ''\t'' || c == -1; } public String next() { return String(); } public interface SpaceCharFilter { public boolean isSpaceChar(int ch); } } static class OutputWriter { private final PrintWriter writer; public OutputWriter(OutputStream outputStream) { writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream))); } public OutputWriter(Writer writer) { this.writer = new PrintWriter(writer); } public void print(Object... objects) { for (int i = 0; i < objects.length; i++) { if (i != 0) writer.print('' ''); writer.print(objects[i]); } } public void printLine(Object... objects) { print(objects); writer.println(); } public void close() { writer.close(); } public void flush() { writer.flush(); } } static InputReader in = new InputReader(System.in); static OutputWriter out = new OutputWriter(System.out); public static long[] sort(long[] a2) { int n = a2.length; ArrayList l = new ArrayList<>(); for (long i : a2) l.add(i); Collections.sort(l); for (int i = 0; i < l.size(); i++) a2[i] = l.get(i); return a2; } public static char[] sort(char[] a2) { int n = a2.length; ArrayList l = new ArrayList<>(); for (char i : a2) l.add(i); Collections.sort(l); for (int i = 0; i < l.size(); i++) a2[i] = l.get(i); return a2; } public static long pow(long x, long y) { long res = 1; while (y > 0) { if (y % 2 != 0) { res = (res * x);// % modulus; y--; } x = (x * x);// % modulus; y = y / 2; } return res; } //GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ public static long gcd(long x, long y) { if (x == 0) return y; else return gcd(y % x, x); } // ******LOWEST COMMON MULTIPLE // ********************************************* public static long lcm(long x, long y) { return (x * (y / gcd(x, y))); } //INPUT PATTERN******************************************************** public static int i() { return in.Int(); } public static long l() { String s = in.String(); return Long.parseLong(s); } public static String s() { return in.String(); } public static int[] readArrayi(int n) { int A[] = new int[n]; for (int i = 0; i < n; i++) { A[i] = i(); } return A; } public static long[] readArray(long n) { long A[] = new long[(int) n]; for (int i = 0; i < n; i++) { A[i] = l(); } return A; } }

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