//--------------------------INPUT READER---------------------------------//
    static class FastIO {
        public BufferedReader br;
        StringTokenizer st = new StringTokenizer("");
 
        public FastIO() { this(System.in); }
        public FastIO(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }
        String next() {
            while (!st.hasMoreTokens()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }
 
        int ni() { return Integer.parseInt(next()); }
        long nl() { return Long.parseLong(next()); }
        double nd() { return Double.parseDouble(next()); }
        String ns() { return next(); }
 
        int[] na(long nn) {
            int n = (int) nn;
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = ni();
            return a;
        }
 
        long[] nal(long nn) {
            int n = (int) nn;
            long[] l = new long[n];
            for(int i = 0; i < n; i++) l[i] = nl();
            return l;
        }
    }
    //-----------------------------------------------------------------------//
 
    //---------------------------PRINTER-------------------------------------//
    static class Printer {
        static PrintWriter w;
        public Printer() {this(System.out);}
        public Printer(OutputStream os) {
            w = new PrintWriter(os);
        }
        public void p(int i) {w.println(i);}
        public void p(long l) {w.println(l);}
        public void p(double d) {w.println(d);}
        public void p(String s) { w.println(s);}
        public void pr(int i) {w.print(i);}
        public void pr(long l) {w.print(l);}
        public void pr(double d) {w.print(d);}
        public void pr(String s) { w.print(s);}
        public void pl() {w.println();}
        public void close() {w.close();}
    }