Submission #1220814

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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 std.typecons, std.math;
// import dcomp.foundation, dcomp.scanner;
// import dcomp.numeric.primitive;
// import dcomp.modint;

alias Mint = ModInt!(10^^9 + 7);
Mint[] p2, fact, ifac;
static this() {
    p2 = new Mint[10000];
    p2[0] = Mint(1);
    foreach (i; 1..10000) {
        p2[i] = p2[i-1]*Mint(2);
    }
    fact = factTable!Mint(10000);
    ifac = invFactTable!Mint(10000);
}

int n;
Mint[] mtc, basec;

void first() {
    mtc = cntMt();
    basec = cntBase();
}

Mint vecvec(int a, int c) {
    Mint[] dp = new Mint[c+1];
    dp[0] = mtc[a];
    Mint sm = 0;
    foreach (i; 0..n+1) {
        if (n+c < a+i) break;
        sm += dp[c]*mtc[i]/basec[i];
        foreach_reverse (j; 0..c+1) {
            dp[j] = dp[j] * (p2[n-a+j] - p2[i]);
            if (j) dp[j] += dp[j-1] * p2[n-a] * (p2[a] - p2[j-1]);
        }
    }
    return sm;
}

int main() {
    auto sc = new Scanner(stdin);
    sc.read(n);
    first();
//    writeln(mtc);
//    writeln(basec);
/*    foreach (c; 0..n+1) {
        Mint sm = 0;
        foreach (a; 0..n+1) {
            sm += vecvec(a, c);
        }
        writeln(c, "=", sm/mtc[c]);
        writeln(); writeln();
    }*/
    bool[][] mt = new bool[][](n, n);
    foreach (i; 0..n) {
        foreach (j; 0..n) {
            int d;
            sc.read(d);
            mt[i][j] = d == 1;
        }
    }
//    writeln(rnk(mt));
    int c = rnk(mt);
    Mint sm = 0;
    foreach (a; 0..n+1) {
        sm += vecvec(a, c);
    }
    writeln(sm/mtc[c]);
    return 0;
}

Mint[] cntMt() {
    auto res = new Mint[n+1];
    res[0] = Mint(1);
    foreach (i; 0..n) {
        foreach_reverse(j; 0..n+1) {
            res[j] *= p2[j];
            if (j) res[j] += res[j-1] * (p2[n] - p2[j-1]);
        }
    }
    return res;
}
Mint[] cntBase() {
    auto res = new Mint[n+1];
    res[0] = Mint(1);
    foreach (i; 1..n+1) {
        res[i] = res[i-1] * (p2[n] - p2[i-1]);
    }
    return res;
}

int rnk(bool[][] mt) {
    int c = 0;
    foreach (i; 0..n) {
        int ni = -1;
        foreach (j; c..n) {
            if (mt[j][i]) {
                ni = j;
                break;
            }
        }
        if (ni == -1) continue;
        swap(mt[c], mt[ni]);
        foreach (j; c+1..n) {
            if (!mt[j][i]) continue;
            foreach (k; 0..n) {
                mt[j][k] ^= mt[i][k];
            }
        }
        c++;
    }
    return c;
}
/* 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;}
}

unittest {
    static assert( is(ModInt!(uint(1000000000) * 2))); //not overflow
    static assert(!is(ModInt!(uint(1145141919) * 2))); //overflow!
    alias Mint = ModInt!(10^^9+7);
    // negative check
    assert(Mint(-1).v == 10^^9 + 6);
    assert(Mint(-1L).v == 10^^9 + 6);

    Mint a = 48;
    Mint b = Mint.inv(a);
    assert(b.v == 520833337);

    Mint c = Mint(15);
    Mint d = Mint(3);
    assert((c/d).v == 5);
}

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;}
    auto normS(uint x) {return (x<MD)?x:x-MD;}
    auto make(uint x) {DModInt m; m.MD = MD; m.v = x; return m;}
    auto opBinary(string op:"+")(DModInt r) {
        return make(normS(v+r.v));
    }
    auto opBinary(string op:"-")(DModInt r) {
        return make(normS(v+MD-r.v));
    }
    auto opBinary(string op:"*")(DModInt r) {
        return make((long(v)*r.v%MD).to!uint);
    }
    auto opBinary(string op:"/")(DModInt r) {
        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;}
}

unittest {
    alias Mint = DModInt!("default");
    Mint.MD = 10^^9 + 7;
    //negative check
    assert(Mint(-1).v == 10^^9 + 6);
    assert(Mint(-1L).v == 10^^9 + 6);
    Mint a = Mint(48);
    Mint b = Mint.inv(a);
    assert(b.v == 520833337);
    Mint c = Mint(15);
    Mint d = Mint(3);
    assert((c/d).v == 5);
}

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;
}

// optimize
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;
}

unittest {
    import std.stdio;
    alias Mint = ModInt!(10^^9 + 7);
    auto r = factTable!Mint(20);
    Mint a = 1;
    assert(r[0] == Mint(1));
    foreach (i; 1..20) {
        a *= Mint(i);
        assert(r[i] == a);
    }
    auto p = invFactTable!Mint(20);
    foreach (i; 1..20) {
        assert((r[i]*p[i]).v == 1);
    }
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/foundation.d */
// module dcomp.foundation;
//fold(for old compiler)
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);
            }
        }
    }
    unittest {
        import std.stdio;
        auto l = [1, 2, 3, 4, 5];
        assert(l.fold!"a+b"(10) == 25);
    }
}
version (X86) static if (__VERSION__ < 2071) {
    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) {
                //string or char[10] etc
                //todo optimize
                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) {
                    //static
                    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);
        }
    }
}



unittest {
    import std.path : buildPath;
    import std.file : tempDir;
    import std.algorithm : equal;
    import std.stdio : File;
    string fileName = buildPath(tempDir, "kyuridenanmaida.txt");
    auto fout = File(fileName, "w");
    fout.writeln("1 2 3");
    fout.writeln("ab cde");
    fout.writeln("1.0 1.0 2.0");
    fout.close;
    Scanner sc = new Scanner(File(fileName, "r"));
    int a;
    int[2] b;
    char[2] c;
    string d;
    double e;
    double[] f;
    sc.read(a, b, c, d, e, f);
    assert(a == 1);
    assert(equal(b[], [2, 3]));
    assert(equal(c[], "ab"));
    assert(equal(d, "cde"));
    assert(e == 1.0);
    assert(equal(f, [1.0, 2.0]));
}

unittest {
    import std.path : buildPath;
    import std.file : tempDir;
    import std.algorithm : equal;
    import std.stdio : File, writeln;
    import std.datetime;
    string fileName = buildPath(tempDir, "kyuridenanmaida.txt");
    auto fout = File(fileName, "w");
    foreach (i; 0..1_000_000) {
        fout.writeln(3*i, " ", 3*i+1, " ", 3*i+2);
    }
    fout.close;
    writeln("Scanner Speed Test(3*1,000,000 int)");
    StopWatch sw;
    sw.start;
    Scanner sc = new Scanner(File(fileName, "r"));
    foreach (i; 0..500_000) {
        int a, b, c;
        sc.read(a, b, c);
        assert(a == 3*i);
        assert(b == 3*i+1);
        assert(c == 3*i+2);
    }
    foreach (i; 500_000..700_000) {
        int[3] d;
        sc.read(d);
        int a = d[0], b = d[1], c = d[2];
        assert(a == 3*i);
        assert(b == 3*i+1);
        assert(c == 3*i+2);
    }
    foreach (i; 700_000..1_000_000) {
        int[] d;
        sc.read(d);
        assert(d.length == 3);
        int a = d[0], b = d[1], c = d[2];
        assert(a == 3*i);
        assert(b == 3*i+1);
        assert(c == 3*i+2);
    }
    writeln(sw.peek.msecs, "ms");
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/numeric/primitive.d */
// module dcomp.numeric.primitive;

import std.traits;

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

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

unittest {
    assert(pow(3, 5) == 243);
    assert(pow(3, 5, 2) == 486);
}

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

unittest {
    assert(lcm(2, 4) == 4);
    assert(lcm(3, 5) == 15);
    assert(lcm(1, 1) == 1);
    assert(lcm(0, 100) == 0);
}

//a*T[0]+b*T[1]=T[2], T[2]=gcd
//todo: to binary extgcd
T[3] extGcd(T)(in T a, in T b) 
if (!isIntegral!T || isSigned!T) //unsignedはNG
{
    if (b==0) {
        return [1, 0, a];
    } else {
        auto e = extGcd(b, a%b);
        return [e[1], e[0]-a/b*e[1], e[2]];
    }
}

unittest {
    import std.numeric : gcd;
    foreach (i; 0..100) {
        foreach (j; 0..100) {
            auto e = extGcd(i, j);
            assert(e[2] == gcd(i, j));
            assert(e[0] * i + e[1] * j == e[2]);
        }
    }
}

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