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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#301729#7906. Almost ConvexKKT89AC ✓472ms4120kbC++148.4kb2024-01-10 08:49:582024-01-10 08:49:59

Judging History

你现在查看的是最新测评结果

  • [2024-01-10 08:49:59]
  • 评测
  • 测评结果:AC
  • 用时:472ms
  • 内存:4120kb
  • [2024-01-10 08:49:58]
  • 提交

answer

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll myRand(ll B) {
    return (ull)rng() % B;
}
inline double time() {
    return static_cast<long double>(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count()) * 1e-9;
}

// https://onlinejudge.u-aizu.ac.jp/courses/library/4/CGL/all
////////////////////////////////////////////////////////////////////////////////
typedef ll Real;
const Real eps = 0; // 1000 : 10^-8, 10000 : 10^-7
inline int sgn(Real a, Real b = 0) { return (a-b < -eps) ? -1 : (a-b > eps) ? 1 : 0; }
inline Real _sqrt(Real a) { return sqrt(max(a, (Real)0)); }
struct Point {
    Real x, y;
    Point() {}
    Point(Real x, Real y) : x(x), y(y) {}
    Point& operator-=(const Point &p) {
        x -= p.x; y -= p.y;
        return *this;
    }
    Point& operator+=(const Point &p) {
        x += p.x; y += p.y;
        return *this;
    }
    Point& operator*=(Real d) {
        x *= d; y *= d;
        return *this;
    }
    Point& operator/=(Real d) {
        x /= d; y /= d;
        return *this;
    }
    Point operator+ (const Point& p) const {
        Point res(*this); return res += p;
    }
    Point operator- (const Point& p) const {
        Point res(*this); return res -= p;
    }
    Point operator* (Real d) const {
        Point res(*this); return res *= d;
    }
    Point operator/ (Real d) const {
        Point res(*this); return res /= d;
    }
    bool operator< (const Point &p) const {
        return (sgn(x, p.x) < 0 or (sgn(x, p.x) == 0 and sgn(y, p.y) < 0));
    }
    bool operator== (const Point& p) const {
        return (sgn(x - p.x) == 0 and sgn(y - p.y) == 0);
    }
    friend istream &operator>> (istream &is, Point &p) {
        is >> p.x >> p.y; return (is);
    }
    Real norm() { return _sqrt(x*x + y*y); }
    Real norm2() { return (x*x + y*y); }
    Point vec() { return (*this); }
    Point unit() { return (*this)/this->norm(); } // 単位ベクトル
    Point perpendicular() { return {-y, x}; }
    Point normal() { return perpendicular().unit(); } // 法線ベクトル
};

Point vec(Point a, Point b) { return (b - a); }
Real dist(Point a, Point b) { return vec(a, b).norm(); }
Real dot(Point a, Point b) { return a.x*b.x + a.y*b.y; }
Real cross(Point a, Point b) { return a.x*b.y - a.y*b.x; }

// 線分
struct Segment : array<Point,2> {
    Segment() {}
    Segment(Point a, Point b) { at(0) = a, at(1) = b; }
    Point vec() { return (at(1) - at(0)); }
    Real length() { return vec().norm(); }
    friend istream &operator>> (istream &is, Segment &s) {
        is >> s[0] >> s[1]; return (is);
    }
};
// 直線
struct Line : Segment {
    Line() {}
    Line(Point a, Point b) : Segment(a, b) {}
    Line(Segment s) : Line(s[0], s[1]) {}
};

int ccw(Point a, Point b, Point c) {
    b -= a; c -= a;
    if (sgn(cross(b, c)) == 1) return 1; // a,b,c 反時計回り
    if (sgn(cross(b, c)) == -1) return -1; // a,b,c 時計周り
    if (sgn(dot(b, c)) == -1) return 2; // c,a,b 一直線上
    if (sgn(c.norm() - b.norm()) == 1) return -2; // a,b,c 一直線上
    return 0; // a,c,b 一直線上
}

// 多角形ライブラリ
struct Polygon : public vector<Point> {
    Polygon() {}
    Polygon(int n) { this->resize(n); }
    Polygon(vector<Point> init) {
        this->resize(init.size());
        for (int i = 0; i < (int)init.size(); ++i) { (*this)[i] = init[i]; }
    }
    Polygon(initializer_list<Point> init) : Polygon(vector<Point> (init.begin(), init.end())) {}
    void rev() { if(sgn(area()) == -1) reverse(this->begin(), this->end()); }
    // 多角形の符号付き面積(反時計回りが正)
    Real area() {
        int n = this->size(); Real s = 0;
        for (int i = 0; i < n; ++i) {
            s += cross((*this)[i], (*this)[(i+1) % n]);
        }
        return s * 0.5;
    }
    // 多角形の凸性判定(反時計周りを仮定)
    bool is_convex() {
        int n = this->size();
        for (int i = 0; i < n; ++i) {
            if (ccw((*this)[i], (*this)[(i+1) % n], (*this)[(i+2) %n]) == -1) return false;
        }
        return true;
    }
    enum Type { OUT, ON, IN };
};

// 凸包 (線分上の点を含めるかどうか)
Polygon convex_full(vector<Point> ps, bool ONSEG = false) {
    int n = (int)ps.size();
    if (n <= 2) return ps;
    sort(ps.begin(), ps.end());
    int k = 0; // 凸包の頂点数
    Polygon qs(2*n); // 構築中の凸包
    auto check = [&](int _ccw) {
        return ONSEG ? _ccw == -1 : _ccw <= 0;
    };
    for (int i = 0; i < n; qs[k++] = ps[i++]) {
        while (k >= 2 and check(ccw(qs[k-2], qs[k-1], ps[i]))) k--;
    }
    for (int i = n-2, t = k+1; i >= 0; qs[k++] = ps[i--]) {
        while (k >= t and check(ccw(qs[k-2], qs[k-1], ps[i]))) k--;
    }
    qs.resize(k-1);
    return qs;
}

int arg_area(Point p){
    if(p.y < 0) return 2;
    else if(p.x < 0) return 1;
    else return 0;
}
// 整数範囲の偏角ソート 同一点ないと仮定
// 同一偏角の場合は原点に近い方を優先
bool arg_comp(Point a, Point b){
    int ap = arg_area(a), bp = arg_area(b);
    if(ap != bp) return ap < bp;
    auto crs = cross(a, b);
    if(crs == 0) return abs(a.x)+abs(a.y) < abs(b.x)+abs(b.y);
    else return crs > 0;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n; cin >> n;
    vector<Point> ps(n);
    for (int i = 0; i < n; ++i) {
        cin >> ps[i];
    }
    auto convex = convex_full(ps);
    int m = convex.size();
    vector<bool> cov(n);
    for (int i = 0; i < m; ++i) {
        for (int j = 0; j < n; ++j) {
            if (ps[j] == convex[i]) cov[j] = true;
        }
    }
    int res = 1;
    for (int i = 0; i < m; ++i) {
        if (n == m) break;
        auto p1 = convex[i];
        auto p2 = convex[(i+1)%m];
        int idx = 0;
        vector<pair<Point,int>> pre,bac;
        pre.push_back({convex[(i-1+m)%m]-p1, -1});
        bac.push_back({convex[(i+2)%m]-p2, -1});
        for (int j = 0; j < n; ++j) {
            if (cov[j]) continue;
            pre.push_back({ps[j]-p1, idx});
            bac.push_back({ps[j]-p2, idx});
            idx += 1;
        }
        sort(pre.begin(), pre.end(), [&](auto i, auto j){
            return arg_comp(i.first, j.first);
        });
        sort(bac.begin(), bac.end(), [&](auto i, auto j){
            return arg_comp(i.first, j.first);
        });
//        cout << p1.x << " " << p1.y << " " << p2.x <<  " " << p2.y << endl;
        vector<int> v;
        for (int j = 0; j < pre.size(); ++j) {
            if (pre[j].second == -1) {
                int id = j;
                for (int k = 1; k < pre.size(); ++k) {
                    id -= 1;
                    if (id == -1) id += pre.size();
//                    cout << pre[id].first.x << "," << pre[id].first.y << " ";
                    v.push_back(pre[id].second);
                }
            }
        }
//        cout << endl;
        for (int j = 0; j < bac.size(); ++j) {
            if (bac[j].second == -1) {
                int id = j;
                for (int k = 1; k < bac.size(); ++k) {
                    id -= 1;
                    if (id == -1) id += bac.size();
//                    cout << bac[id].first.x << "," << bac[id].first.y << " ";
                    v.push_back(bac[id].second);
                }
            }
        }
//        cout << endl;
        set<int> ok,ng;
        queue<int> que;
        for (int j = 0; j < v.size(); ++j) {
//            cout << v[j] << " ";
            if (ok.find(v[j]) == ok.end() and ng.find(v[j]) == ng.end()) {
                ok.insert(v[j]);
                que.push(v[j]);
            }
            else {
                if (ng.find(v[j]) != ng.end()) {
                    ng.erase(v[j]);
                }
                else {
                    res += 1;
                    ok.erase(v[j]);
                    while (que.front() != v[j]) {
                        ng.insert(que.front());
                        ok.erase(que.front());
                        que.pop();
                    }
                    que.pop();
                }
            }
        }
//        cout << endl;
    }
    cout << res << endl;
}

这程序好像有点Bug,我给组数据试试?

详细

Test #1:

score: 100
Accepted
time: 0ms
memory: 3788kb

input:

7
1 4
4 0
2 3
3 1
3 5
0 0
2 4

output:

9

result:

ok 1 number(s): "9"

Test #2:

score: 0
Accepted
time: 1ms
memory: 3792kb

input:

5
4 0
0 0
2 1
3 3
3 1

output:

5

result:

ok 1 number(s): "5"

Test #3:

score: 0
Accepted
time: 1ms
memory: 3552kb

input:

3
0 0
3 0
0 3

output:

1

result:

ok 1 number(s): "1"

Test #4:

score: 0
Accepted
time: 1ms
memory: 3680kb

input:

6
0 0
3 0
3 2
0 2
1 1
2 1

output:

7

result:

ok 1 number(s): "7"

Test #5:

score: 0
Accepted
time: 1ms
memory: 3832kb

input:

4
0 0
0 3
3 0
3 3

output:

1

result:

ok 1 number(s): "1"

Test #6:

score: 0
Accepted
time: 57ms
memory: 4120kb

input:

2000
86166 617851
383354 -277127
844986 386868
-577988 453392
-341125 -386775
-543914 -210860
-429613 606701
-343534 893727
841399 339305
446761 -327040
-218558 -907983
787284 361823
950395 287044
-351577 -843823
-198755 138512
-306560 -483261
-487474 -857400
885637 -240518
-297576 603522
-748283 33...

output:

718

result:

ok 1 number(s): "718"

Test #7:

score: 0
Accepted
time: 52ms
memory: 4120kb

input:

2000
571314 -128802
-57762 485216
-713276 485201
-385009 -844644
371507 403789
338703 -272265
-913641 438001
-792118 -481524
709494 213762
-913577 432978
-397111 709021
840950 328210
-843628 452653
-20721 126607
-107804 -338102
930109 -89787
-949115 -76479
-862141 455623
991761 94852
-635475 625573
...

output:

658

result:

ok 1 number(s): "658"

Test #8:

score: 0
Accepted
time: 36ms
memory: 3912kb

input:

2000
-510540 -289561
-602648 -189950
-403224 944455
-369582 -41334
358122 -598933
-817147 470207
-440180 -735160
-705634 61719
319062 897001
-905089 -755682
-408371 -520115
-423336 548115
-590242 835990
208155 883477
-202087 142035
-71545 411206
570690 -673204
-228451 -903435
-732876 -570271
-246755...

output:

309

result:

ok 1 number(s): "309"

Test #9:

score: 0
Accepted
time: 24ms
memory: 3976kb

input:

2000
-532115 566389
138405 49337
398814 -97324
116833 113216
381728 877609
222402 641022
109920 952381
-113880 395181
13780 -572931
-676608 605202
-74328 -503839
-207767 926500
-663270 -146303
197877 280349
275865 -663892
-630214 3286
973786 304855
-493735 841584
394901 -505975
757960 204724
-373328...

output:

239

result:

ok 1 number(s): "239"

Test #10:

score: 0
Accepted
time: 31ms
memory: 3896kb

input:

2000
512636 509804
-661126 -592269
755566 -721837
-878213 441853
-236050 -89069
-181220 155656
203391 691764
940154 260513
747075 373881
620423 840991
-409624 335472
270937 -710659
-751290 -673585
250341 -193243
-250535 618887
-739996 543936
-547741 -213681
-82920 -364319
-611672 737719
930798 46731...

output:

1025

result:

ok 1 number(s): "1025"

Test #11:

score: 0
Accepted
time: 23ms
memory: 3876kb

input:

2000
943353 817289
237151 899722
682851 -464873
854225 205354
834550 257948
-260874 298196
-224572 -269157
-667301 881130
-45920 -696359
-634337 792620
-408527 -947513
582880 172669
921645 839423
833813 721080
-836662 -287230
-55783 -408594
108996 -122012
365647 -789544
313812 833502
970009 -737736
...

output:

218

result:

ok 1 number(s): "218"

Test #12:

score: 0
Accepted
time: 5ms
memory: 4076kb

input:

2000
619248 227987
-252490 -553032
148050 -479727
-333707 -591482
-40488 -503144
561909 255624
-402541 -798967
-245811 -610006
-146584 -517935
226433 -92580
-81939 -828480
72540 -845547
502613 220323
66708 -573015
601886 258752
406443 257854
232970 -671600
-37023 -683767
602339 456757
-440096 -71899...

output:

7

result:

ok 1 number(s): "7"

Test #13:

score: 0
Accepted
time: 8ms
memory: 3932kb

input:

2000
-602451 2956
85982 141739
-185932 -208897
-716095 58215
-468047 155612
-791626 -3105
75700 -484098
609608 -304849
689485 -106857
533177 -285261
-659400 -241162
-369302 165482
406663 265940
-353843 -788313
805885 -75440
-571955 -60471
351360 -81373
-510926 -59456
591713 179588
534794 -118
201630...

output:

66

result:

ok 1 number(s): "66"

Test #14:

score: 0
Accepted
time: 11ms
memory: 4028kb

input:

2000
41203 -675424
-158994 366628
-133859 -595680
435466 687630
687811 -35017
314337 133049
-384711 444777
54850 -760922
526166 282618
572292 94793
-324003 621393
-30308 242225
612969 -231837
-56628 -892609
-492077 58749
29597 -349591
198510 219502
380955 -59845
839171 -40068
88185 -820614
-572977 -...

output:

43

result:

ok 1 number(s): "43"

Test #15:

score: 0
Accepted
time: 14ms
memory: 3948kb

input:

2000
-814040 46114
-324077 -522697
388552 -604274
-252898 43028
-757069 141507
413462 -649779
-281915 -316285
-498931 -573214
-408766 670792
-271435 -393170
87187 731739
89312 -853584
-768680 -307261
-185324 234729
-70493 -354866
16452 164338
-650791 -518077
851196 -259322
-85395 -509349
241593 5074...

output:

129

result:

ok 1 number(s): "129"

Test #16:

score: 0
Accepted
time: 27ms
memory: 3892kb

input:

2000
23103 -796677
-148322 67634
-525131 -446626
2672 584671
-712789 -69579
-91150 -429393
-375635 -487235
-680553 -370975
793181 -383683
-234131 -462420
-734705 -171834
322671 -355011
760005 224249
700248 -352775
416862 -125857
-497951 717254
677084 -451876
-220123 616240
525973 -144881
-300828 553...

output:

1466

result:

ok 1 number(s): "1466"

Test #17:

score: 0
Accepted
time: 65ms
memory: 3920kb

input:

2000
-185174 470373
-772343 -70370
-182314 851727
661615 -250979
-581175 527646
332025 141502
-659052 -506788
-378459 -553180
11233 162287
469975 -572356
679074 217029
-137967 727723
581696 140544
452574 -319370
120895 129820
772655 -330960
122860 823902
-786221 147543
-206152 -373647
-212943 4820
6...

output:

2801

result:

ok 1 number(s): "2801"

Test #18:

score: 0
Accepted
time: 121ms
memory: 3976kb

input:

2000
-718158 695879
655921 595312
-509080 -860718
540612 244159
-83221 -865654
-460513 -542465
102321 -775593
328552 799263
-284269 -725108
152140 549502
-108610 465054
-97837 -449762
-772869 -171472
293831 -711723
508617 -157976
170737 323070
544222 385453
-633043 -233165
-620164 -459706
507218 338...

output:

14445

result:

ok 1 number(s): "14445"

Test #19:

score: 0
Accepted
time: 211ms
memory: 3988kb

input:

2000
-587991 -165467
-530325 -5525
-574943 180654
-496535 -748102
-436469 -160646
110285 237070
-822862 -141480
-177189 327799
-424868 331309
-999274 38095
-745710 192605
-234174 -804258
586432 -176239
-626756 499109
-562606 826724
890245 455480
-32262 -298900
550800 516690
-588632 -368654
405331 -3...

output:

64358

result:

ok 1 number(s): "64358"

Test #20:

score: 0
Accepted
time: 400ms
memory: 3892kb

input:

2000
441575 -414673
651578 -449237
287355 -489950
606811 -30288
-733692 679481
-652568 89883
-360110 616801
190405 -368787
-352383 935855
118240 73038
-374899 -927065
-22183 -491455
-146229 638417
998825 -48442
-374469 243261
988830 149043
-778607 -291542
-277026 -167975
372912 -405043
535321 425727...

output:

233885

result:

ok 1 number(s): "233885"

Test #21:

score: 0
Accepted
time: 465ms
memory: 3888kb

input:

2000
-369265 -366669
-225059 -65255
750236 -107534
-252341 967638
533029 -79205
-482639 504243
-164616 -477455
-219649 975578
222020 297565
-548636 -836060
595498 -345235
-971961 -235140
179392 983777
747498 664263
-458850 -513884
-456639 186799
508542 -359953
630300 5257
-294961 -599723
999627 2729...

output:

430546

result:

ok 1 number(s): "430546"

Test #22:

score: 0
Accepted
time: 466ms
memory: 3868kb

input:

2000
-586906 -809654
-279647 960102
-279925 501031
-76716 526333
-277891 -599253
171606 -289251
565124 -825005
-125381 -163097
-71257 -202933
999551 29949
286017 -698748
257733 358898
6047 18648
283230 -959051
221238 -975219
686818 32684
368089 -929790
-689242 449329
-547431 836850
612952 -790120
-9...

output:

484966

result:

ok 1 number(s): "484966"

Test #23:

score: 0
Accepted
time: 472ms
memory: 3920kb

input:

2000
-360385 -932803
6402 -568575
477942 -878390
361387 -497256
-383874 -126116
-838786 214745
157834 -987465
955879 293759
-91170 -521309
262250 964999
883045 -469287
350745 823160
999731 -23179
-791215 8792
208002 153508
-553609 549966
-345358 591962
-613852 198594
81698 996657
803702 98789
201163...

output:

513300

result:

ok 1 number(s): "513300"

Test #24:

score: 0
Accepted
time: 467ms
memory: 3832kb

input:

2000
-996201 87077
834777 -550587
-316381 948632
750921 -473436
-170208 -985408
-98642 17818
735787 -677212
80294 -996771
-420703 594219
995302 -96813
997685 68003
-680287 396657
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-64...

output:

528222

result:

ok 1 number(s): "528222"

Test #25:

score: 0
Accepted
time: 461ms
memory: 3768kb

input:

2000
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output:

527976

result:

ok 1 number(s): "527976"

Test #26:

score: 0
Accepted
time: 465ms
memory: 3764kb

input:

2000
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output:

536419

result:

ok 1 number(s): "536419"

Test #27:

score: 0
Accepted
time: 459ms
memory: 3824kb

input:

2000
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4...

output:

541774

result:

ok 1 number(s): "541774"

Test #28:

score: 0
Accepted
time: 448ms
memory: 3784kb

input:

2000
125380 -992108
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output:

554369

result:

ok 1 number(s): "554369"

Test #29:

score: 0
Accepted
time: 455ms
memory: 3956kb

input:

2000
877194 480134
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output:

556266

result:

ok 1 number(s): "556266"

Test #30:

score: 0
Accepted
time: 444ms
memory: 3792kb

input:

2000
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output:

578226

result:

ok 1 number(s): "578226"

Test #31:

score: 0
Accepted
time: 420ms
memory: 3756kb

input:

2000
588463 808523
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output:

599788

result:

ok 1 number(s): "599788"

Test #32:

score: 0
Accepted
time: 412ms
memory: 4028kb

input:

2000
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output:

607941

result:

ok 1 number(s): "607941"

Test #33:

score: 0
Accepted
time: 415ms
memory: 3888kb

input:

2000
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output:

605021

result:

ok 1 number(s): "605021"

Test #34:

score: 0
Accepted
time: 400ms
memory: 3896kb

input:

2000
748836 662754
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output:

609148

result:

ok 1 number(s): "609148"

Test #35:

score: 0
Accepted
time: 398ms
memory: 3752kb

input:

2000
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output:

612907

result:

ok 1 number(s): "612907"

Test #36:

score: 0
Accepted
time: 391ms
memory: 3816kb

input:

2000
710449 252021
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61275...

output:

613033

result:

ok 1 number(s): "613033"

Test #37:

score: 0
Accepted
time: 382ms
memory: 4020kb

input:

2000
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output:

613525

result:

ok 1 number(s): "613525"

Test #38:

score: 0
Accepted
time: 385ms
memory: 3808kb

input:

2000
-31467 999504
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output:

609202

result:

ok 1 number(s): "609202"

Test #39:

score: 0
Accepted
time: 375ms
memory: 3808kb

input:

2000
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18...

output:

610683

result:

ok 1 number(s): "610683"

Test #40:

score: 0
Accepted
time: 367ms
memory: 3884kb

input:

2000
315983 611022
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output:

606866

result:

ok 1 number(s): "606866"

Test #41:

score: 0
Accepted
time: 356ms
memory: 3784kb

input:

2000
827570 -561361
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output:

605654

result:

ok 1 number(s): "605654"

Test #42:

score: 0
Accepted
time: 351ms
memory: 3768kb

input:

2000
660227 -171320
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output:

607199

result:

ok 1 number(s): "607199"

Test #43:

score: 0
Accepted
time: 344ms
memory: 3988kb

input:

2000
-404720 641654
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output:

603919

result:

ok 1 number(s): "603919"

Test #44:

score: 0
Accepted
time: 342ms
memory: 3740kb

input:

2000
-599904 800071
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output:

598805

result:

ok 1 number(s): "598805"

Test #45:

score: 0
Accepted
time: 337ms
memory: 3800kb

input:

2000
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output:

598251

result:

ok 1 number(s): "598251"

Test #46:

score: 0
Accepted
time: 325ms
memory: 3872kb

input:

2000
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1...

output:

588592

result:

ok 1 number(s): "588592"

Test #47:

score: 0
Accepted
time: 309ms
memory: 3948kb

input:

2000
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output:

580267

result:

ok 1 number(s): "580267"

Test #48:

score: 0
Accepted
time: 299ms
memory: 3960kb

input:

2000
-999844 17617
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7...

output:

574822

result:

ok 1 number(s): "574822"

Test #49:

score: 0
Accepted
time: 299ms
memory: 3664kb

input:

2000
-642241 766502
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output:

569661

result:

ok 1 number(s): "569661"

Test #50:

score: 0
Accepted
time: 111ms
memory: 3868kb

input:

2000
-628838 -357590
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output:

324930

result:

ok 1 number(s): "324930"

Test #51:

score: 0
Accepted
time: 46ms
memory: 3892kb

input:

2000
973483 228755
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output:

180726

result:

ok 1 number(s): "180726"

Test #52:

score: 0
Accepted
time: 21ms
memory: 3800kb

input:

2000
-784353 -620314
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output:

95123

result:

ok 1 number(s): "95123"

Test #53:

score: 0
Accepted
time: 11ms
memory: 3928kb

input:

2000
-378825 -925468
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output:

39222

result:

ok 1 number(s): "39222"

Test #54:

score: 0
Accepted
time: 9ms
memory: 3720kb

input:

2000
-982363 -186982
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-414704 ...

output:

19811

result:

ok 1 number(s): "19811"

Test #55:

score: 0
Accepted
time: 2ms
memory: 3712kb

input:

2000
-944717 -327884
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output:

1

result:

ok 1 number(s): "1"

Extra Test:

score: 0
Extra Test Passed