import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } alias Pt = Tuple!(long, "x", long, "y"); void main() { try { for (; ; ) { const N = readInt(); auto P = new Pt[N]; foreach (i; 0 .. N) { P[i].x = readLong(); P[i].y = readLong(); } if (N <= 1) { writeln(1 << N); continue; } Pt[] dirs; foreach (i; 0 .. N) foreach (j; 0 .. N) { if (i != j) { long dx = P[j].x - P[i].x; long dy = P[j].y - P[i].y; const g = gcd(abs(dx), abs(dy)); dirs ~= Pt(dy / g, -dx / g); } } dirs.sort!((const(Pt) p, const(Pt) q) { const sp = (p.y > 0) ? 1 : (p.y < 0) ? 3 : (p.x > 0) ? 0 : 2; const sq = (q.y > 0) ? 1 : (q.y < 0) ? 3 : (q.x > 0) ? 0 : 2; return ((sp != sq) ? (sp < sq) : (p.x * q.y - p.y * q.x > 0)); }); dirs = dirs.uniq.array; const dirsLen = cast(int)(dirs.length); alias PJ = Tuple!(int, "p", int, "j"); PJ[] pjs; foreach (j; 0 .. dirsLen) { real t0 = atan2(cast(real)(dirs[j].y), cast(real)(dirs[j].x)); real t1 = atan2(cast(real)(dirs[(j + 1) % $].y), cast(real)(dirs[(j + 1) % $].x)); if (t0 > t1) { t1 += 2.0L * PI; } const tMid = (t0 + t1) / 2.0L; const xMid = cos(tMid); const yMid = sin(tMid); alias Entry = Tuple!(real, "val", int, "key"); auto es = new Entry[N]; foreach (i; 0 .. N) { es[i] = Entry(xMid * P[i].x + yMid * P[i].y, i); } es.sort; debug { writefln("(%s, %s): %s", xMid, yMid, es.map!"a.key"); } int p; foreach (i; 0 .. N) { if (i > 0) { pjs ~= PJ(p, j); } p |= 1 << es[i].key; } } pjs.sort; const pjsLen = cast(int)(pjs.length); alias PJJ = Tuple!(int, "p", int, "j0", int, "j1"); PJJ[] pjjs; for (int e = 0, f; e < pjsLen; e = f) { for (f = e; f < pjsLen && pjs[e].p == pjs[f].p; ++f) {} int j0 = -1, j1 = -1; foreach (g; e .. f - 1) { if (pjs[g].j + 1 < pjs[g + 1].j) { j0 = pjs[g + 1].j; j1 = pjs[g].j + 1 + dirsLen; } } if (j0 == -1) { j0 = pjs[e].j; j1 = pjs[f - 1].j + 1; } pjjs ~= PJJ(pjs[e].p, j0, j1); } const pjjsLen = cast(int)(pjjs.length); debug { writeln("pjjs = ", pjjs); } auto used = new bool[1 << N]; used[0] = used[$ - 1] = true; foreach (k0; 0 .. pjjsLen) { used[pjjs[k0].p] = true; } foreach (k0; 0 .. pjjsLen) foreach (k1; k0 .. pjjsLen) { used[pjjs[k0].p | pjjs[k1].p] = true; } foreach (k0; 0 .. pjjsLen) foreach (k1; k0 .. pjjsLen) foreach (k2; k1 .. pjjsLen) { auto ts = [pjjs[k0], pjjs[k1], pjjs[k2]]; ts = ts ~ ts; bool ok = true; foreach (l; 0 .. 3) { const lb = ts[l].j0; const ub = ts[l].j0 + dirsLen / 2; if ( ((lb <= ts[l + 1].j0 && ts[l + 1].j1 <= ub) || (lb <= ts[l + 1].j0 + dirsLen && ts[l + 1].j1 + dirsLen <= ub)) && ((lb <= ts[l + 2].j0 && ts[l + 2].j1 <= ub) || (lb <= ts[l + 2].j0 + dirsLen && ts[l + 2].j1 + dirsLen <= ub)) ) { ok = false; break; } } if (ok) { used[ts[0].p | ts[1].p | ts[2].p] = true; } } const ans = cast(int)(used.count(true)); writeln(ans); } } catch (EOFException e) { } }