Submission #1561105

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Source Code Expand

/+ dub.sdl:
    name "A"
    dependency "dcomp" version=">=0.6.0"
+/

import std.stdio, std.algorithm, std.range, std.conv;
// import dcomp.foundation, dcomp.scanner, dcomp.numeric.primitive;
// import dcomp.modint, dcomp.geo;

alias Mint = ModInt!998244353;
alias P = Point2D!int;

import std.typecons;

Mint[] fact, iFac;
static this() {
    fact = factTable!Mint(10000);
    iFac = invFactTable!Mint(10000);
}
Mint C(int n, int k) {
    if (n < 0 || n < k) return Mint(0);
    return Mint(0);
}
Mint choose3(int n) {
    if (n <= 2) return Mint(0);
    Mint sm = pow(Mint(2), n);
    sm -= Mint(n * (n-1) / 2);
    sm -= Mint(n);
    sm -= Mint(1);
    return sm;
}

int main() {
    auto sc = new Scanner(stdin);
    int n;
    sc.read(n);
    P[] p = new P[n];
    foreach (i; 0..n) {
        sc.read(p[i].x, p[i].y);
    }
    Mint res = choose3(n);

    bool[][] g = new bool[][](n, n);
    foreach (i; 0..n) {
        foreach (j; i+1..n) {
            if (g[i][j]) continue;
            int[] v = [i, j];
            foreach (k; 0..n) {
                if (i == k || j == k) continue;
                if (cross(p[j]-p[i], p[k]-p[i]) == 0) {
                    v ~= k;
                }
            }
            res -= choose3(v.length.to!int);
            foreach (d; v) {
                foreach (e; v) {
                    g[d][e] = g[e][d] = true;
                }
            }
        }
    }
    writeln(res);
    return 0;
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/modint.d */
// module dcomp.modint;

// import dcomp.numeric.primitive;

 
struct ModInt(uint MD) if (MD < int.max) {
    import std.conv : to;
    uint v;
    this(int v) {this(long(v));}
    this(long v) {this.v = (v%MD+MD)%MD;}
    static auto normS(uint x) {return (x<MD)?x:x-MD;}
    static auto make(uint x) {ModInt m; m.v = x; return m;}
     
    auto opBinary(string op:"+")(ModInt r) const {return make(normS(v+r.v));}
     
    auto opBinary(string op:"-")(ModInt r) const {return make(normS(v+MD-r.v));}
     
    auto opBinary(string op:"*")(ModInt r) const {return make((long(v)*r.v%MD).to!uint);}
     
    auto opBinary(string op:"/")(ModInt r) const {return this*inv(r);}
    auto opOpAssign(string op)(ModInt r) {return mixin ("this=this"~op~"r");}
     
    static ModInt inv(ModInt x) {return ModInt(extGcd!int(x.v, MD)[0]);}
    string toString() {return v.to!string;}
}

 
 

 

 
struct DModInt(string name) {
    import std.conv : to;
    static uint MD;
    uint v;
    this(int v) {this(long(v));}
    this(long v) {this.v = ((v%MD+MD)%MD).to!uint;}
    static auto normS(uint x) {return (x<MD)?x:x-MD;}
    static auto make(uint x) {DModInt m; m.MD = MD; m.v = x; return m;}
     
    auto opBinary(string op:"+")(DModInt r) const {return make(normS(v+r.v));}
     
    auto opBinary(string op:"-")(DModInt r) const {return make(normS(v+MD-r.v));}
     
    auto opBinary(string op:"*")(DModInt r) const {return make((long(v)*r.v%MD).to!uint);}
     
    auto opBinary(string op:"/")(DModInt r) const {return this*inv(r);}
    auto opOpAssign(string op)(DModInt r) {return mixin ("this=this"~op~"r");}
     
    static DModInt inv(DModInt x) {
        return DModInt(extGcd!int(x.v, MD)[0]);
    }
    string toString() {return v.to!string;}
}

 
 

 

template isModInt(T) {
    const isModInt =
        is(T : ModInt!MD, uint MD) || is(S : DModInt!S, string s);
}


T[] factTable(T)(size_t length) if (isModInt!T) {
    import std.range : take, recurrence;
    import std.array : array;
    return T(1).recurrence!((a, n) => a[n-1]*T(n)).take(length).array;
}

 
T[] invFactTable(T)(size_t length) if (isModInt!T) {
    import std.algorithm : map, reduce;
    import std.range : take, recurrence, iota;
    import std.array : array;
    auto res = new T[length];
    res[$-1] = T(1) / iota(1, length).map!T.reduce!"a*b";
    foreach_reverse (i, v; res[0..$-1]) {
        res[i] = res[i+1] * T(i+1);
    }
    return res;
}

T[] invTable(T)(size_t length) if (isModInt!T) {
    auto f = factTable!T(length);
    auto invf = invFactTable!T(length);
    auto res = new T[length];
    foreach (i; 1..length) {
        res[i] = invf[i] * f[i-1];
    }
    return res;
}

 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/foundation.d */
// module dcomp.foundation;
 
static if (__VERSION__ <= 2070) {
    template fold(fun...) if (fun.length >= 1) {
        auto fold(R, S...)(R r, S seed) {
            import std.algorithm : reduce;
            static if (S.length < 2) {
                return reduce!fun(seed, r);
            } else {
                import std.typecons : tuple;
                return reduce!fun(tuple(seed), r);
            }
        }
    }
     
}
version (X86) static if (__VERSION__ < 2071) {
    import core.bitop : bsf, bsr, popcnt;
    int bsf(ulong v) {
        foreach (i; 0..64) {
            if (v & (1UL << i)) return i;
        }
        return -1;
    }
    int bsr(ulong v) {
        foreach_reverse (i; 0..64) {
            if (v & (1UL << i)) return i;
        }
        return -1;   
    }
    int popcnt(ulong v) {
        int c = 0;
        foreach (i; 0..64) {
            if (v & (1UL << i)) c++;
        }
        return c;
    }
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/scanner.d */
// module dcomp.scanner;

 
class Scanner {
    import std.stdio : File;
    import std.conv : to;
    import std.range : front, popFront, array, ElementType;
    import std.array : split;
    import std.traits : isSomeChar, isStaticArray, isArray; 
    import std.algorithm : map;
    File f;
    this(File f) {
        this.f = f;
    }
    char[512] lineBuf;
    char[] line;
    private bool succ() {
        import std.range.primitives : empty, front, popFront;
        import std.ascii : isWhite;
        while (true) {
            while (!line.empty && line.front.isWhite) {
                line.popFront;
            }
            if (!line.empty) break;
            if (f.eof) return false;
            line = lineBuf[];
            f.readln(line);
        }
        return true;
    }

    private bool readSingle(T)(ref T x) {
        import std.algorithm : findSplitBefore;
        import std.string : strip;
        import std.conv : parse;
        if (!succ()) return false;
        static if (isArray!T) {
            alias E = ElementType!T;
            static if (isSomeChar!E) {
                 
                 
                auto r = line.findSplitBefore(" ");
                x = r[0].strip.dup;
                line = r[1];
            } else {
                auto buf = line.split.map!(to!E).array;
                static if (isStaticArray!T) {
                     
                    assert(buf.length == T.length);
                }
                x = buf;
                line.length = 0;
            }
        } else {
            x = line.parse!T;
        }
        return true;
    }
    int read(T, Args...)(ref T x, auto ref Args args) {
        if (!readSingle(x)) return 0;
        static if (args.length == 0) {
            return 1;
        } else {
            return 1 + read(args);
        }
    }
}


 
 

 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/geo.d */
// module dcomp.geo;

import std.traits;

struct Point2D(T) {
    T[2] d;
    this(T x, T y) {this.d = [x, y];}
    this(T[2] d) {this.d = d;}
    @property ref inout(T) x() inout {return d[0];}
    @property ref inout(T) y() inout {return d[1];}
    ref inout(T) opIndex(size_t i) inout {return d[i];}
    auto opBinary(string op:"+")(Point2D r) const {return Point2D(x+r.x, y+r.y);}
    auto opBinary(string op:"-")(Point2D r) const {return Point2D(x-r.x, y-r.y);}
    static if (isFloatingPoint!T) {
        T abs() {
            import std.math : sqrt;
            return (x*x+y*y).sqrt;
        }
        T arg() {
            import std.math : atan2;
            return atan2(y, x);
        }
    }
}

T dot(T)(in Point2D!T l, in Point2D!T r) {
    return l[0]*l[0] + l[1]*r[1];
}

T cross(T)(in Point2D!T l, in Point2D!T r) {
    return l[0]*r[1] - l[1]*r[0];
}

 

 
 
int argcmp(T)(Point2D!T l, Point2D!T r) if (isIntegral!T) {
    int sgn(Point2D!T p) {
        if (p[1] < 0) return -1;
        if (p[1] > 0) return 1;
        if (p[0] < 0) return 2;
        return 0;
    }
    int lsgn = sgn(l);
    int rsgn = sgn(r);
    if (lsgn < rsgn) return -1;
    if (lsgn > rsgn) return 1;

    T x = cross(l, r);
    if (x > 0) return -1;
    if (x < 0) return 1;

    return 0;
}


 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/numeric/primitive.d */
// module dcomp.numeric.primitive;

import std.traits;
import std.bigint;

 
T pow(T, U)(T x, U n) if (!isFloatingPoint!T && (isIntegral!U || is(U == BigInt))) {
    return pow(x, n, T(1));
}

 
T pow(T, U)(T x, U n, T e) if (isIntegral!U || is(U == BigInt)) {
    while (n) {
        if (n & 1) e *= x;
        x *= x;
        n /= 2;
    }
    return e;
}

 

 
T lcm(T)(in T a, in T b) {
    import std.numeric : gcd;
    return a / gcd(a,b) * b;
}

 
 

 
 
T[3] extGcd(T)(in T a, in T b) 
if (!isIntegral!T || isSigned!T)  
{
    if (b==0) {
        return [T(1), T(0), a];
    } else {
        auto e = extGcd(b, a%b);
        return [e[1], e[0]-a/b*e[1], e[2]];
    }
}

 
 

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