Submission #1220263

---

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;
// import dcomp.foundation, dcomp.scanner;
// import dcomp.algorithm;
// import dcomp.array;
// import dcomp.graph.scc;

int vc;
int[2][] edges;

struct Node {
    Node* l, r;
    int sz;
    int id;
    this(int sz) {
        this.sz = sz;
        id = vc; vc++;
        if (sz == 1) return;
        l = new Node(sz/2);
        r = new Node(sz-sz/2);
    }
    void addEdge(int a, int b, int p) {
        if (a <= 0 && sz <= b) {
            edges ~= [p, id];
            return;
        }
        if (b <= 0 || sz <= a) return;
        l.addEdge(a, b, p);
        r.addEdge(a-sz/2, b-sz/2, p);
    }
    void set(int k, int p) {
        id = vc; vc++;
        if (sz == 1) {
            edges ~= [id, p];
            return;
        }
        if (k < sz/2) {
            l.set(k, p);
        } else {
            r.set(k-sz/2, p);
        }
        edges ~= [id, l.id];
        edges ~= [id, r.id];
    }
}

int main() {
    auto sc = new Scanner(stdin);
    int n;
    sc.read(n);
    int[] l, r;
    sc.read(l, r);
    vc = n;
    {
        int[2][] f = iota(n).map!(i => [l[i]-i, i].fixed).array
            ~ iota(n).map!(i => [r[i]-i, n+i].fixed).array;

        f.sort!((a, b) => cmp(a[], b[]) == -1);

        auto seg = new Node(n);
        foreach (ev; f) {
            int i = ev[1]%n;
            if (ev[1] >= n) {
                //que
                seg.addEdge(0, i, i);
//                writeln("que-left ", i);
            } else {
                //set
                seg.set(i, i);
//                writeln("add-left ", i);
            }
        }
    }
    
    {
        int[2][] f = iota(n).map!(i => [l[i]+i, i].fixed).array
            ~ iota(n).map!(i => [r[i]+i, n+i].fixed).array;

        f.sort!((a, b) => cmp(a[], b[]) == -1);

        auto seg = new Node(n);
        foreach (ev; f) {
            int i = ev[1]%n;
            if (ev[1] >= n) {
                //que
                seg.addEdge(i+1, n, i);
//                writeln("que-right ", i);
            } else {
                //set
                seg.set(i, i);
//                writeln("add-right ", i);
            }
        }
    }
    
//    writeln(edges);

    alias Edge = Tuple!(int, "to");
    Edge[][] g = new Edge[][](vc);
    foreach (e; edges) {
        g[e[0]] ~= Edge(e[1]);
    }
    auto sccInfo = scc(g);

//    writeln(sccInfo);

    int m = sccInfo.groups.length.to!int;

    int[][] ng = new int[][](m);
    int[] wei = new int[](m);
    foreach (i; 0..n) {
        wei[sccInfo.id[i]]++;
    }
    foreach (e; edges) {
        int x = sccInfo.id[e[0]];
        int y = sccInfo.id[e[1]];
        if (x == y) continue;
        ng[x] ~= y;
    }
//    writeln(wei);
//    writeln(ng);
    foreach_reverse (i; 0..m) {
        int ma = 0;
        foreach (d; ng[i]) {
            ma = max(ma, wei[d]);
        }
        wei[i] += ma;
    }
//    writeln(wei);
    writeln(wei.maximum);
    return 0;
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/graph/scc.d */
// module dcomp.graph.scc;

// import dcomp.array;
// import dcomp.graph.primitive;
// import dcomp.container.deque;

struct SCC {
    int[] id; // vertex id -> scc id
    int[][] groups; // scc id -> scc vertexs
    this(int n) {
        id = new int[n];
    }
}

SCC scc(T)(T g) {
    import std.range;
    import std.algorithm : each, map, min, reverse;
    import std.conv : to;
    int n = g.length.to!int;
    auto sccInfo = SCC(n);
    with (sccInfo) {
        bool[] inS = new bool[n];
        int[] low = new int[n], ord = new int[n]; ord[] = -1;
        int time = 0;
        Deque!int st;
        int bufC = 0;
        FastAppender!(int[]) buf; buf.reserve(n);
        FastAppender!(int[][]) gBuf;
        void dfs(int v) {
            low[v] = ord[v] = time++;
            st.insertBack(v);
            inS[v] = true;
            foreach (e; g[v]) {
                if (ord[e.to] == -1) {
                    dfs(e.to);
                    low[v] = min(low[v], low[e.to]);
                } else if (inS[e.to]) {
                    low[v] = min(low[v], ord[e.to]);
                }
            }
            if (low[v] == ord[v]) {
                int p = st.length.to!int - 1;
                while (true) {
                    int u = st.back; st.removeBack;
                    buf ~= u;
                    if (u == v) break;
                }
                auto gr = buf.data[bufC..$];
                bufC = buf.length.to!int;
                gr.each!(x => inS[x] = false);
                gBuf ~= gr;
            }
        }
        foreach (i; 0..n) {
            if (ord[i] == -1) dfs(i);
        }
        groups = gBuf.data;
        reverse(groups);
        groups.each!((i, v) => v.each!(x => id[x] = i.to!int));
    }
    return sccInfo;
}

unittest {
    import std.algorithm, std.conv, std.stdio, std.range;
    import std.random;
    import std.typecons;
    import std.datetime;

    struct E {int to;}

    writeln("SCC Random1000");
    void f() {
        int n = uniform(1, 50);
        int p = uniform(1, 50);
        E[][] g = new E[][n];
        bool[][] naive = new bool[][](n, n);
        foreach (i; 0..n) {
            foreach (j; 0..n) {
                if (i == j) continue;
                if (uniform(0, 100) < p) {
                    g[i] ~= E(j);
                    naive[i][j] = true;
                }
            }
        }

        auto sccInfo = scc(g);

        foreach (k; 0..n) {
            foreach (i; 0..n) {
                foreach (j; 0..n) {
                    naive[i][j] |= naive[i][k] && naive[k][j];
                }
            }
        }

        foreach (i; 0..n) {
            int iid = sccInfo.id[i];
            assert(sccInfo.groups[iid].find(i).empty == false);
            foreach (j; i+1..n) {
                bool same = sccInfo.id[i] == sccInfo.id[j];
                if (same) {
                    assert(naive[i][j] && naive[j][i]);
                } else {
                    assert(!naive[i][j] || !naive[j][i]);                    
                    if (sccInfo.id[i] < sccInfo.id[j]) {
                        assert(!naive[j][i]);
                    } else {
                        assert(!naive[i][j]);
                    }
                }
            }
        }
    }
    auto ti = benchmark!(f)(1000);
    writeln(ti[0].msecs, "ms");
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/algorithm.d */
// module dcomp.algorithm;

import std.range.primitives;
import std.traits : isFloatingPoint, isIntegral;

//[0,0,0,...,1,1,1]で、初めて1となる場所を探す。pred(l) == 0, pred(r) == 1と仮定
T binSearch(alias pred, T)(T l, T r) if (isIntegral!T) {
    while (r-l > 1) {
        T md = (l+r)/2;
        if (!pred(md)) l = md;
        else r = md;
    }
    return r;
}

T binSearch(alias pred, T)(T l, T r, int cnt = 60) if (isFloatingPoint!T) {
    foreach (i; 0..cnt) {
        T md = (l+r)/2;
        if (!pred(md)) l = md;
        else r = md;
    }
    return r;
}

Rotator!Range rotator(Range)(Range r) {
    return Rotator!Range(r);
}

struct Rotator(Range)
if (isForwardRange!Range && hasLength!Range) {
    size_t cnt;
    Range start, now;
    this(Range r) {
        cnt = 0;
        start = r.save;
        now = r.save;
    }
    this(this) {
        start = start.save;
        now = now.save;
    }
    @property bool empty() {
        return now.empty;
    }
    @property auto front() {
        assert(!now.empty);
        import std.range : take, chain;
        return chain(now, start.take(cnt));
    }
    @property Rotator!Range save() {
        return this;
    }
    void popFront() {
        cnt++;
        now.popFront;
    }
}


E minimum(alias pred = "a < b", Range, E = ElementType!Range)(Range range, E seed)
if (isInputRange!Range && !isInfinite!Range) {
    import std.algorithm, std.functional;
    return reduce!((a, b) => binaryFun!pred(a, b) ? a : b)(seed, range);
}

ElementType!Range minimum(alias pred = "a < b", Range)(Range range) {
    assert(!range.empty, "range must not empty");
    auto e = range.front; range.popFront;
    return minimum!pred(range, e);
}

E maximum(alias pred = "a < b", Range, E = ElementType!Range)(Range range, E seed)
if (isInputRange!Range && !isInfinite!Range) {
    import std.algorithm, std.functional;
    return reduce!((a, b) => binaryFun!pred(a, b) ? b : a)(seed, range);
}

ElementType!Range maximum(alias pred = "a < b", Range)(Range range) {
    assert(!range.empty, "range must not empty");
    auto e = range.front; range.popFront;
    return maximum!pred(range, e);
}

unittest {
    assert(minimum([2, 1, 3]) == 1);
    assert(minimum!"a > b"([2, 1, 3]) == 3);
    assert(minimum([2, 1, 3], -1) == -1);
    assert(minimum!"a > b"([2, 1, 3], 100) == 100);

    assert(maximum([2, 1, 3]) == 3);
    assert(maximum!"a > b"([2, 1, 3]) == 1);
    assert(maximum([2, 1, 3], 100) == 100);
    assert(maximum!"a > b"([2, 1, 3], -1) == -1);
}

bool[ElementType!Range] toMap(Range)(Range r) {
    import std.algorithm : each;
    bool[ElementType!Range] res;
    r.each!(a => res[a] = true);
    return res;
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/container/deque.d */
// module dcomp.container.deque;

struct Deque(T) {
    import core.exception : RangeError;
    import core.memory : GC;
    import std.range : ElementType, isInputRange;
    import std.traits : isImplicitlyConvertible;

    struct Payload {
        T *d;
        size_t st, length, cap;
        @property bool empty() const { return length == 0; }
        alias opDollar = length;
        ref inout(T) opIndex(size_t i) inout {
            version(assert) if (length <= i) throw new RangeError();
            return d[(st+i >= cap) ? (st+i-cap) : st+i];
        }
        private void expand() {
            import std.algorithm : max;
            assert(length == cap);
            auto nc = max(size_t(4), 2*cap);
            T* nd = cast(T*)GC.malloc(nc * T.sizeof);
            foreach (i; 0..length) {
                nd[i] = this[i];
            }
            d = nd; st = 0; cap = nc;
        }
        void clear() {
            st = length = 0;
        }
        void insertFront(T v) {
            if (length == cap) expand();
            if (st == 0) st += cap;
            st--; length++;
            this[0] = v; 
        }
        void insertBack(T v) {
            if (length == cap) expand();
            length++;
            this[length-1] = v; 
        }
        void removeFront() {
            assert(!empty, "Deque.removeFront: Deque is empty");        
            st++; length--;
            if (st == cap) st = 0;
        }
        void removeBack() {
            assert(!empty, "Deque.removeBack: Deque is empty");        
            length--;
        }        
    }
    struct RangeT(A) {
        alias T = typeof(*(A.p));
        alias E = typeof(A.p.d[0]);
        T *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!Deque;
    alias ConstRange = RangeT!(const Deque);
    alias ImmutableRange = RangeT!(immutable Deque);

    Payload *p;
    private void I() { if (!p) p = new Payload(); }
    private void C() const {
        version(assert) if (!p) throw new RangeError();
    }
    //some value
    this(U)(U[] values...) if (isImplicitlyConvertible!(U, T)) {I;
        p = new Payload();
        foreach (v; values) {
            insertBack(v);
        }
    }
    //range
    this(Range)(Range r)
    if (isInputRange!Range &&
    isImplicitlyConvertible!(ElementType!Range, T) &&
    !is(Range == T[])) {I;
        p = new Payload();
        foreach (v; r) {
            insertBack(v);
        }
    }
    
    @property bool empty() const { return (!p || p.empty); }
    @property size_t length() const { return (p ? p.length : 0); }
    alias opDollar = length;
    ref inout(T) opIndex(size_t i) inout {C; return (*p)[i]; }
    ref inout(T) front() inout {C; return (*p)[0]; }
    ref inout(T) back() inout {C; return (*p)[$-1]; }
    void clear() { if (p) p.clear(); }
    void insertFront(T v) {I; p.insertFront(v); }
    void insertBack(T v) {I; p.insertBack(v); }
    void removeFront() {C; p.removeFront(); }
    void removeBack() {C; p.removeBack(); }
    Range opSlice() {I; return Range(p, 0, length); }
}

unittest {
    import std.algorithm : equal;
    import std.range.primitives : isRandomAccessRange;
    import std.container.util : make;
    auto q = make!(Deque!int);
    assert(isRandomAccessRange!(typeof(q[])));

    //insert,remove
    assert(equal(q[], new int[](0)));
    q.insertBack(1);
    assert(equal(q[], [1]));
    q.insertBack(2);
    assert(equal(q[], [1, 2]));
    q.insertFront(3);
    assert(equal(q[], [3, 1, 2]) && q.front == 3);
    q.removeFront;
    assert(equal(q[], [1, 2]) && q.length == 2);
    q.insertBack(4);
    assert(equal(q[], [1, 2, 4]) && q.front == 1 && q.back == 4 && q[$-1] == 4);
    q.insertFront(5);
    assert(equal(q[], [5, 1, 2, 4]));

    //range
    assert(equal(q[][1..3], [1, 2]));
    assert(equal(q[][][][], q[]));
    //const range
    const auto rng = q[];
    assert(rng.front == 5 && rng.back == 4);
    
    //reference type
    auto q2 = q;
    q2.insertBack(6);
    q2.insertFront(7);
    assert(equal(q[], q2[]) && q.length == q2.length);

    //construct with make
    auto a = make!(Deque!int)(1, 2, 3);
    auto b = make!(Deque!int)([1, 2, 3]);
    assert(equal(a[], b[]));
}

unittest {
    import std.algorithm : equal;
    import std.range.primitives : isRandomAccessRange;
    import std.container.util : make;
    auto q = make!(Deque!int);
    q.clear();
    assert(equal(q[], new int[0]));
    foreach (i; 0..100) {
        q.insertBack(1);
        q.insertBack(2);
        q.insertBack(3);
        q.insertBack(4);
        q.insertBack(5);    
        assert(equal(q[], [1,2,3,4,5]));
        q.clear();
        assert(equal(q[], new int[0]));
    }

}
unittest {
    Deque!int a;
    Deque!int b;
    a.insertFront(2);
    assert(b.length == 0);
}

unittest {
    import std.algorithm : equal;
    import std.range : iota;
    Deque!int a;
    foreach (i; 0..100) {
        a.insertBack(i);
    }
    assert(equal(a[], iota(100)));
}
/* 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/graph/primitive.d */
// module dcomp.graph.primitive;

import std.range : ElementType;
alias EdgeType(R) = ElementType!(ElementType!R);
/* 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/array.d */
// module dcomp.array;

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

//this is not reference type!(please attention to copy)
struct FastAppender(A) {
    import std.algorithm : max;
    import std.range.primitives : ElementEncodingType;
    import core.stdc.string : memcpy;

    private alias T = ElementEncodingType!A;
    private T* _data;
    private size_t len, cap;
    @property size_t length() {return len;}
    void reserve(size_t nlen) {
        import core.memory : GC;
        if (nlen <= cap) return;
        
        void* nx = GC.malloc(nlen * T.sizeof);

        cap = nlen;
        if (len) memcpy(nx, _data, len * T.sizeof);
        _data = cast(T*)(nx);
    }
    void opOpAssign(string op : "~")(T item) {
        if (len == cap) {
            reserve(max(4, cap*2));
        }
        _data[len++] = item;
    }
    void clear() {
        len = 0;
    }    
    T[] data() {
        return (_data) ? _data[0..len] : null;
    }
}

unittest {
    import std.stdio, std.algorithm;
    auto u = FastAppender!(int[])();
    u ~= 4; u ~= 5;
    assert(equal(u.data, [4, 5]));
}

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