package adv2016; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.Comparator; import java.util.InputMismatchException; public class N461_2 { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(); long[][][] es = new long[3][n+1][]; int[] ep = new int[3]; for(int i = 0;i < 3;i++){ es[i][ep[i]++] = new long[]{1, 1}; } for(int i = 0;i < n;i++){ int t = ni(); int x = ni(), y = ni(); es[t][ep[t]++] = new long[]{x, x+y}; } Arrays.sort(es[1], 0, ep[1], comp); Arrays.sort(es[2], 0, ep[2], comp); long ret = 0; for(int i = 0;i < ep[0];i++){ long[] low0 = {es[0][i][1]-es[0][i][0], es[0][i][1]}; int lowp = ep[2]; int remp = ep[2]; for(int j = 0;j < ep[1];j++){ long[] ad = add(es[0][i], es[1][j]); if(ad[0] < ad[1])continue; long[] low1 = {es[1][j][1]-es[1][j][0], es[1][j][1]}; long[] low = null; if(compare(low0, low1) < 0){ low = low1; }else{ low = low0; } // low:decreasing // rem:decreasing while(lowp-1 >= 0 && compare(low, es[2][lowp-1]) <= 0)lowp--; long[] rem = sub(new long[]{2, 1}, ad); ret += ep[2]-lowp; while(remp-1 >= 0 && compare(rem, es[2][remp-1]) < 0)remp--; if(remp >= 1 && lowp <= remp-1 && compare(rem, es[2][remp-1]) == 0){ ret--; } } } out.println(ret); } public static Comparator comp = (a, b) -> Long.signum(a[0]*b[1]-a[1]*b[0]); public static int lowerBound(long[][] es, int p, long[] r) { int low = -1, high = p; while(high-low > 1){ int h = high+low>>>1; if(Long.compare(r[0]*es[h][1], r[1]*es[h][0]) <= 0){ high = h; }else{ low = h; } } return high; } public static long[] reduce(long[] f) { if(f[1] == 0) { // n/0 f[0] = 1; }else if(f[0] == 0) { // 0/n f[1] = 1; }else { if(f[1] < 0) { // -a/-b ->a/b f[0] = -f[0]; f[1] = -f[1]; } long a = Math.abs(f[0]), b = f[1]; while (b > 0) { long c = a; a = b; b = c % b; } f[0] /= a; f[1] /= a; } return f; } public static long[] add(long[] a, long[] b){ return reduce(new long[]{a[0]*b[1]+a[1]*b[0], a[1]*b[1]}); } public static long[] sub(long[] a, long[] b){ return reduce(new long[]{a[0]*b[1]-a[1]*b[0], a[1]*b[1]}); } public static long[] mul(long[] a, long[] b){ return reduce(new long[]{a[0]*b[0], a[1]*b[1]}); } public static long[] div(long[] a, long[] b){ return reduce(new long[]{a[0]*b[1], a[1]*b[0]}); } public static int compare(long[] a, long[] b){return Long.signum(a[0] * b[1] - a[1] * b[0]);} public static long[] min(long[] a, long[] b){ return compare(a, b) <= 0 ? a : b; } public static long[] max(long[] a, long[] b){ return compare(a, b) >= 0 ? a : b; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-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(); } public static void main(String[] args) throws Exception { new N461_2().run(); } private 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 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))){ // when nextLine, (isSpaceChar(b) && 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 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 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[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } 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(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }