Submission #1831361

---

Source Code Expand

/+ dub.sdl:
    name "A"
    dependency "dcomp" version=">=0.8.0"
+/

import std.stdio, std.algorithm, std.range, std.conv;
// import dcomp.foundation, dcomp.scanner;

// import dcomp.modint;
alias Mint = ModInt!(10^^9 + 7);

int main() {
    Scanner sc = new Scanner(stdin);

    int n;
    sc.read(n);
    int[][] g = new int[][n];
    foreach (i; 1..n) {
        int p;
        sc.read(p); p--;
        g[p] ~= i;
    }

    int[] sz = new int[n];
    Mint[4][][] dp = new Mint[4][][n];
    void dfs(int p) {
        sz[p] = 1;        
        foreach (d; g[p]) {
            dfs(d);
            sz[p] += sz[d];
        }
        dp[p] = new Mint[4][](sz[p]+1);
        auto ndp = dp[p];
        ndp[0][0] = Mint(1);
        int msz = 1;
        foreach (d; g[p]) {
            foreach_reverse (kl; 0..msz+sz[d]+1) {
                foreach_reverse (fg; 0..4) {
                    Mint sm = 0;
                    foreach_reverse (k; 0..min(kl+1, msz+1)) {
                        auto l = kl-k;
                        if (sz[d] < l) break;
                        foreach_reverse (f; 0..4) {
                            if (~fg & f) continue;
                            auto g = fg^f;
                            sm += ndp[k][f] * dp[d][l][g];
                        }
                    }
                    ndp[kl][fg] = sm;
                }
            }
            msz += sz[d];
        }
//        writeln("fl ", p, " ", ndp);
        foreach_reverse (i; 0..sz[p]+1) {
            ndp[i][0] += ndp[i][1] + ndp[i][2] + ndp[i][3];
            if (i) ndp[i][1] = ndp[i-1][1] + ndp[i-1][0];
            else ndp[i][1] = Mint(0);
            if (i) ndp[i][2] = ndp[i-1][2] + ndp[i-1][0];
            else ndp[i][2] = Mint(0);
            ndp[i][3] = Mint(0);
        }
    }
    dfs(0);
//    writeln(dp.map!(x => x.to!string).join("\n"));

    auto fact = factTable!Mint(10000);
    Mint ans = 0;
    foreach (i; 0..n+1) {
        Mint freq = (i % 2) ? Mint(-1) : Mint(1);
        ans += freq * dp[0][i][0] * fact[n-i];
    }
    writeln(ans);
    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((ulong(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() const {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((ulong(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/numeric/primitive.d */
// module dcomp.numeric.primitive;

import std.traits;
import std.bigint;

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

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

 


T powMod(T, U, V)(T x, U n, V md)
if (isIntegral!U || is(U == BigInt)) {
    T r = T(1);
    while (n) {
        if (n & 1) r = (r*x)%md;
        x = (x*x)%md;
        n >>= 1;
    }
    return r % md;
}

ulong ulongPowMod(U)(ulong x, U n, ulong md)
if (isIntegral!U || is(U == BigInt)) {
//     import dcomp.int128;
    x %= md;
    ulong r = 1;
    while (n) {
        if (n & 1) {
            r = mul128(r, x).mod128(md);
        }
        x = mul128(x, x).mod128(md);
        n >>= 1;
    }
    return r % md;
}

 
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]];
    }
}

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

struct StackPayload(T, size_t MIN = 4) {
    import core.exception : RangeError;
    import std.algorithm : max;
    import std.conv;
    import std.range.primitives : ElementEncodingType;
    import core.stdc.string : memcpy;

    private T* _data;
    private uint len, cap;
     
    bool empty() const { return len == 0; }
    @property size_t length() const { return len; }
    alias opDollar = length;

    ref inout(T) opIndex(size_t i) inout { return _data[i]; }
    ref inout(T) front() inout { return _data[0]; }
    ref inout(T) back() inout { assert(len); return _data[len-1]; }
    
     
    void reserve(size_t nlen) {
        import core.memory : GC;
        if (nlen <= cap) return;
        
        void* nx = GC.malloc(nlen * T.sizeof);

        cap = nlen.to!uint;
        if (len) memcpy(nx, _data, len * T.sizeof);
        _data = cast(T*)(nx);
    }
    void free() {
        import core.memory : GC;
        GC.free(_data);
    }
     
    void opOpAssign(string op : "~")(T item) {
        if (len == cap) {
            reserve(max(MIN, cap*2));
        }
        _data[len++] = item;
    }
     
    void insertBack(T item) {
        this ~= item;
    }
     
    void removeBack() {
        len--;
    }
     
    void clear() {
        len = 0;
    }
     
    inout(T)[] data() inout {
        return (_data) ? _data[0..len] : null;
    }

    static struct RangeT(A) {
        import std.traits : CopyTypeQualifiers;
        alias E = CopyTypeQualifiers!(A, T);
        A *p;
        size_t a, b;
        @property bool empty() const { return b <= a; }
        @property size_t length() const { return b-a; }
        @property RangeT save() { return RangeT(p, a, b); }
        @property RangeT!(const A) save() const {
            return typeof(return)(p, a, b);
        }
        alias opDollar = length;
        @property ref inout(E) front() inout { return (*p)[a]; }
        @property ref inout(E) back() inout { return (*p)[b-1]; }
        void popFront() {
            version(assert) if (empty) throw new RangeError();
            a++;
        }
        void popBack() {
            version(assert) if (empty) throw new RangeError();
            b--;
        }
        ref inout(E) opIndex(size_t i) inout { return (*p)[i]; }
        RangeT opSlice() { return this.save; }
        RangeT opSlice(size_t i, size_t j) {
            version(assert) if (i > j || a + j > b) throw new RangeError();
            return typeof(return)(p, a+i, a+j);
        }
        RangeT!(const A) opSlice() const { return this.save; }
        RangeT!(const A) opSlice(size_t i, size_t j) const {
            version(assert) if (i > j || a + j > b) throw new RangeError();
            return typeof(return)(p, a+i, a+j);
        }
    }
    alias Range = RangeT!(StackPayload!T);
    alias ConstRange = RangeT!(const StackPayload!T);
    alias ImmutableRange = RangeT!(immutable StackPayload!T);
}

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

version(LDC) {
    pragma(LDC_inline_ir)
        R inlineIR(string s, R, P...)(P);
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/scanner.d */
// module dcomp.scanner;

// import dcomp.container.stackpayload;

 
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 succW() {
        import std.range.primitives : empty, front, popFront;
        import std.ascii : isWhite;
        while (!line.empty && line.front.isWhite) {
            line.popFront;
        }
        return !line.empty;
    }
    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;
            line = lineBuf[];
            f.readln(line);
            if (!line.length) return false;
        }
        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 static if (isStaticArray!T) {
                foreach (i; 0..T.length) {
                    bool f = succW();
                    assert(f);
                    x[i] = line.parse!E;
                }
            } else {
                StackPayload!E buf;
                while (succW()) {
                    buf ~= line.parse!E;
                }
                x = buf.data;
            }
        } 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/foundation.d */
// module dcomp.foundation;

 
static if (__VERSION__ <= 2070) {
    /*
    Copied by https://github.com/dlang/phobos/blob/master/std/algorithm/iteration.d
    Copyright: Andrei Alexandrescu 2008-.
    License: $(HTTP boost.org/LICENSE_1_0.txt, Boost License 1.0).
    */
    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);
            }
        }
    }
     
}

import core.bitop : popcnt;
static if (!__traits(compiles, popcnt(ulong.max))) {
    public import core.bitop : popcnt;
    int popcnt(ulong v) {
        return popcnt(cast(uint)(v)) + popcnt(cast(uint)(v>>32));
    }
}

bool poppar(ulong v) {
    v^=v>>1; v^=v>>2;
    v&=0x1111111111111111UL;
    v*=0x1111111111111111UL;
    return ((v>>60) & 1) != 0;
}


 
T[N] fixed(T, size_t N)(T[N] a) {return a;}

 
 

/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/int128.d */
 

// module dcomp.int128;

version(LDC) {
//     import dcomp.ldc.inline;
}

version(LDC) version(X86_64) {
    version = LDC_IR;
}

 
ulong[2] mul128(ulong a, ulong b) {
    ulong[2] res;
    version(LDC_IR) {
        ulong upper, lower;
        inlineIR!(`
            %r0 = zext i64 %0 to i128 
            %r1 = zext i64 %1 to i128
            %r2 = mul i128 %r1, %r0
            %r3 = trunc i128 %r2 to i64
            %r4 = lshr i128 %r2, 64
            %r5 = trunc i128 %r4 to i64
            store i64 %r3, i64* %2
            store i64 %r5, i64* %3`, void)(a, b, &lower, &upper);
        return [lower, upper];
    } else version(D_InlineAsm_X86_64) {
        ulong upper, lower;
        asm {
            mov RAX, a;
            mul b;
            mov lower, RAX;
            mov upper, RDX;
        }
        return [lower, upper];
    } else {
        ulong B = 2UL^^32;
        ulong[2] a2 = [a % B, a / B];
        ulong[2] b2 = [b % B, b / B];
        ulong[4] c;
        foreach (i; 0..2) {
            foreach (j; 0..2) {
                c[i+j] += a2[i] * b2[j] % B;
                c[i+j+1] += a2[i] * b2[j] / B;
            }
        }
        foreach (i; 0..3) {
            c[i+1] += c[i] / B;
            c[i] %= B;
        }
        return [c[0] + c[1] * B, c[2] + c[3] * B];
    }
}

 

 
ulong div128(ulong[2] a, ulong b) {
    version(LDC_IR) {
        return inlineIR!(`
            %r0 = zext i64 %0 to i128
            %r1 = zext i64 %1 to i128
            %r2 = shl i128 %r1, 64
            %r3 = add i128 %r0, %r2
            %r4 = zext i64 %2 to i128
            %r5 = udiv i128 %r3, %r4
            %r6 = trunc i128 %r5 to i64
            ret i64 %r6`,ulong)(a[0], a[1], b);
    } else version(D_InlineAsm_X86_64) {
        ulong upper = a[1], lower = a[0];
        ulong res;
        asm {
            mov RDX, upper;
            mov RAX, lower;
            div b;
            mov res, RAX;
        }
        return res;
    } else {
        if (b == 1) return a[0];
        while (!(b & (1UL << 63))) {
            a[1] <<= 1;
            if (a[0] & (1UL << 63)) a[1] |= 1;
            a[0] <<= 1;
            b <<= 1;
        }
        ulong ans = 0;
        foreach (i; 0..64) {
            bool up = (a[1] & (1UL << 63)) != 0;
            a[1] <<= 1;
            if (a[0] & (1UL << 63)) a[1] |= 1;
            a[0] <<= 1;

            ans <<= 1;
            if (up || b <= a[1]) {
                a[1] -= b;
                ans++;
            }
        }
        return ans;
    }
}


 
ulong mod128(ulong[2] a, ulong b) {
    version(D_InlineAsm_X86_64) {
        ulong upper = a[1], lower = a[0];
        ulong res;
        asm {
            mov RDX, upper;
            mov RAX, lower;
            div b;
            mov res, RDX;
        }
        return res;
    } else {
        return a[0] - div128(a, b) * b;
    }
}

 

/*
This source code generated by dcomp and include dcomp's source code.
dcomp's Copyright: Copyright (c) 2016- Kohei Morita. (https://github.com/yosupo06/dcomp)
dcomp's License: MIT License(https://github.com/yosupo06/dcomp/blob/master/LICENSE.txt)
*/

Submission Info

Compile Error

warning: Linking two modules of different data layouts: '<string>' is '' whereas './Main.d' is 'e-m:e-i64:64-f80:128-n8:16:32:64-S128'

warning: Linking two modules of different data layouts: '<string>' is '' whereas './Main.d' is 'e-m:e-i64:64-f80:128-n8:16:32:64-S128'

Judge Result