package adv2020; import java.io.*; import java.math.BigInteger; import java.util.ArrayDeque; import java.util.Arrays; import java.util.InputMismatchException; import java.util.Queue; import java.util.function.LongBinaryOperator; import java.util.function.LongUnaryOperator; public class Day19_2 { InputStream is; FastWriter out; String INPUT = ""; long[][] pr; long N; int[] primes = sieveEratosthenes(200000); long f(long n, long div, int pid) { if(pid >= primes.length || n < primes[pid]-1){ return 1L; } long ans = 0; int x = pid; for(;n >= (long)(primes[x]-1)*(primes[x]-1);x++) { int p = primes[x]; long m = n / (p-1); long nd = div * (p-1); while (m > 0) { ans += f(m, nd, x + 1); m /= p; nd *= p; } } ans += (div*div <= N+1 ? pr[1][(int)div] : pr[0][(int)n]) - x + 1; // tr(n,div, x, primes[x], (div*div <= N+1 ? pr[1][(int)div] : pr[0][(int)n]) - x, ans, pr[0] ,pr[1]); return ans; } public void solve() { long n = nl(); N = n; pr = countsPrime(n); int[] primes = sieveEratosthenes(pr[0].length+1); for(int i = 1;i < pr[0].length;i++){ if(Arrays.binarySearch(primes, i+1) >= 0){ pr[0][i]++; } } for(int i = 1;i < pr[1].length;i++){ if(BigInteger.valueOf(n/i+1).isProbablePrime(20)){ pr[1][i]++; } } // 2*10^12ぐらい // phi(x)<=n // phi(3x) = 2phi(x) // f(n,p)=f(n,np) + f(n/(p-1),np) + f(n/p(p-1),np) + ... // f(n,p)=1 if n> 5] |= 1 << (i & 31); for (int j = 0; j < sup; j += tp) { for (int i = 0; i < tp && i + j < sup; i++) { isnp[j + i] |= ptn[i]; } } } // 3,5,7 // 2x+3=n int[] magic = {0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14}; int h = n / 2; for (int i = 0; i < sup; i++) { for (int j = ~isnp[i]; j != 0; j &= j - 1) { int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27]; int p = 2 * pp + 3; if (p > n) break; ret[pos++] = p; if ((long) p * p > n) continue; for (int q = (p * p - 3) / 2; q <= h; q += p) isnp[q >> 5] |= 1 << q; } } return Arrays.copyOf(ret, pos); } /** * 乗法的関数の素ベキ上の定義f(p,e)から、正整数上の定義f(x)を出力する * @param f * @param primes * @return */ public static LongUnaryOperator toUnary(LongBinaryOperator f, int[] primes) { return (x) -> { long ret = 1; for(int p : primes){ int e = 0; while(x % p == 0){ e++; x /= p; } if(e > 0)ret = ret * f.applyAsLong(p, e); } if(x > 1)ret = ret * f.applyAsLong(x, 1); return ret; }; } public static long[][] add(long[][] a, long[][] b, int mod) { long[][] c = new long[2][a[0].length]; for(int j = 0;j < 2;j++){ for(int i = 0;i < a[0].length;i++){ c[j][i] = a[j][i] + b[j][i]; if(c[j][i] >= mod)c[j][i] -= mod; } } return c; } public static long[][] add_(long[][] a, long[][] b, int mod) { for(int j = 0;j < 2;j++){ for(int i = 0;i < a[0].length;i++){ a[j][i] += b[j][i]; if(a[j][i] >= mod)a[j][i] -= mod; } } return a; } public static long[][] mul(long[][] a, long x, int mod) { long[][] c = new long[2][a[0].length]; for(int j = 0;j < 2;j++){ for(int i = 0;i < a[0].length;i++){ c[j][i] = a[j][i] * x % mod; } } return c; } public static long[][] mul_(long[][] a, long x, int mod) { for(int j = 0;j < 2;j++){ for(int i = 0;i < a[0].length;i++){ a[j][i] = a[j][i] * x % mod; } } return a; } public static long[][] mul(long[][] a, long x) { long[][] c = new long[2][a[0].length]; for(int j = 0;j < 2;j++){ for(int i = 0;i < a[0].length;i++){ c[j][i] = a[j][i] * x; } } return c; } public static long[][] mul_(long[][] a, long x) { for(int j = 0;j < 2;j++){ for(int i = 0;i < a[0].length;i++){ a[j][i] = a[j][i] * x; } } return a; } public static long[][] countsPrime(long n) { return sumsOnPrimes(n, x -> 1, x -> x); } public static long[][] sumsOnPrimes(long n, LongUnaryOperator f, LongUnaryOperator S) { int B = (int)Math.sqrt(n); int[] primes = sieveEratosthenes(B); long[] low = new long[B+1]; long[] high = new long[B+1]; for(int i = 1;i <= B;i++) { low[i] = S.applyAsLong(i); high[i] = S.applyAsLong(n/i); } for(int p : primes) { long fp = f.applyAsLong(p); int isup = (int)Math.min(n/p/p, B); for(int i = 1;i <= isup;i++) { if((long)i*p <= B) { high[i] -= fp * (high[i*p] - low[p-1]); }else { high[i] -= fp * (low[(int)(n/i/p)] - low[p-1]); } } for(int i = B;i >= (long)p*p;i--) { low[i] -= fp * (low[i/p] - low[p-1]); } } for(int i = 1;i <= B;i++) { low[i]--; high[i]--; } return new long[][] {low, high}; } public static void main(String[] args) { new Day19_2().run(); } public void run() { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } // private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln(); return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }