1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
#include <bits/stdc++.h>
#include <unistd.h>
#include "message.h"
using namespace std;

using u64 = uint64_t;
using i64 = int64_t;
using ci64 = int64_t const;
using vi = vector<i64>;
using vvi = vector<vector<i64>>;
using cvi = vector<i64> const;
using cvvi = vector<vector<i64>> const;
using D = double;

// {{{ utils
vi split_range(i64 l, i64 r, i64 n) {
    vi res;
    for (i64 i = 1; i <= n; i++)
        res.push_back(l + (r - l) * i / n);
    return res;
}
pair<i64, i64> get_split(i64 l, i64 r, i64 n, i64 k) {
    auto const split = split_range(l, r, n);
    if (k == 0)
        return make_pair(0, split[0] - 1);
    return make_pair(split[k - 1], split[k] - 1);
}
// }}}

int const v_max = 1000000;
i64 n;
i64 node_id;
i64 nodes_cnt;

pair<i64, i64> my_split() {
    return get_split(0, n, nodes_cnt, node_id);
}
pair<i64, i64> max_split() {
    return {0, n - 1};
}

// print tuples {{{
template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& t) {
    return os << '[' << t.first << ',' << t.second << ']';
}
void print_tpl_helper(ostream&, bool) {}
template <typename T, typename ...Ts>
void print_tpl_helper(ostream& os, bool first, const T& v, const Ts& ...vs) {
    if (!first){os << ',';} os << v; print_tpl_helper(os, false, vs...);
}
template <typename ...Ts>
ostream& print_struct(ostream& os, const char* classname, const Ts& ...vs) {
        // todo: named fields
    os << classname << '('; print_tpl_helper(os, true, vs...); return os << ')';
}
struct Example {
    char symbol;
    u64 val;
    friend ostream& operator<<(ostream& os, const Example& elem) {
        return print_struct(os, "Op", elem.symbol, elem.val);
    }
};
// }}}
// print containers {{{
template <typename It>
void print(ostream& os, It begin, It end, u64 len, u64 limit = 17) {
    u64 count = 0;
    os << "{";
    while (begin != end && count < limit) {
        os << "(" << *begin << ")";
        count++;
        begin++;
    }
    if (begin != end)
        os << "... " << len << " total";
    os << "}";
}
#define MAKE_PRINTER_1(container) \
template <typename T> ostream& operator<<(ostream& os, const container<T>& t) { print(os, t.begin(), t.end(), t.size()); return os; }
#define MAKE_PRINTER_2(container) \
template <typename T1, typename T2> \
ostream& operator<<(ostream& os, const container<T1, T2>& t) { \
    print(os, t.begin(), t.end(), t.size()); \
    return os; \
}
MAKE_PRINTER_1(vector)
MAKE_PRINTER_2(map)
MAKE_PRINTER_1(set)
MAKE_PRINTER_2(unordered_map)
MAKE_PRINTER_1(unordered_set)
#undef MAKE_PRINTER_1
#undef MAKE_PRINTER_2
// }}}
// read/write {{{
template <typename T> struct identity { const T& operator()(const T& t) const { return t; } };
#define PRINTERS(FNAME, OUTP) \
    template <typename T> void FNAME(const T& t) { OUTP << t << ' '; } \
    void FNAME##ln() { OUTP << '\n'; } \
    template <typename T> void FNAME##ln(const T& t) { OUTP << t << '\n'; } \
    template <typename T, typename F = identity<typename T::value_type>> \
    void FNAME##v(const T& t, F f = F()) { for (const auto& e : t) FNAME(f(e)); FNAME##ln(); }
PRINTERS(print, cout)
#ifdef DEBUG_PRINTS
    PRINTERS(dprint, cerr)
#else
# define dprint(...)
# define dprintv(...)
# define dprintln(...)
#endif
/// }}}
// range, len, max {{{
i64 max(i64 a, i64 b) { return a < b ? b : a; }
vi range(i64 start, i64 end) {
    vi v;
    for (i64 i = start; i < end; i++)
        v.push_back(i);
    return v;
}
vi range(i64 end) { return range(0, end); }
template <typename DS>
i64 len(DS t) { return (i64)t.size(); }
// }}}
// {{{ teatr.h
#ifdef MY_COMPUTER
int const _n = 10000;


//int GetN() { return 1000 * 1000 * 100; }
//int GetElement(int i) {
//    // 2497220719002543
//    using ll = long long;
////    return 1 + i / 100;
//return 1 + (((ll)i * 27) + i & (i %113) + ((i % 37) ^ (i % 20)) * 3571) % 1000000;
//}
//int GetN() { return 100 * 1000 * 1000; }
//int GetElement(int i) {
//if (i < 100 * 1000 * 1000 - 3) return 1 + i / 100;
//else return 100 * 1000 * 1000 - i;
//// 299999394
//}
//int GetN() { return int(1e8); }
// 2499912950050000
//int GetElement(int i) { return (i * 1ll * i) % int(1e6) + 1; }
//
int GetN() { return int(1e8); }
int GetElement(int i) { return (int(1e8) - i - 1) / 100 + 1; }
 // 4999995000000000 , dunno if good

//
//int GetN() {
//    ++mock_counter;
//    if (mock_counter == mock_counter_limit) {
//        usleep(1000);
//        mock_counter = 0;
//    }
//    if (len(mock_data))
//        return len(mock_data);
//    return _n;
//}
//int GetElement(int k) {
//    ++mock_counter;
//    if (mock_counter == mock_counter_limit) {
//        usleep(1000);
//        mock_counter = 0;
//    }
//    if (k < len(mock_data))
//        return mock_data[k];
//    return 1 + ((i64)k * 13213ll + 123ll) % v_max;
//}
#else
//i64 mock_counter;
//i64 const mock_counter_limit = 29000;
//
//void slow_down() {
//    ++mock_counter;
//    if (mock_counter == mock_counter_limit) {
//        usleep(1000);
//        mock_counter = 0;
//    }
//}
//
//int GetN() {
//    slow_down();
//    return 100 * 1000 * 1000;
//}
//int GetElement(int i) {
//    slow_down();
//    using ll = long long;
//    return 1 + i / 100;
//}
#include "teatr.h"
#endif
// }}}
void read_benchmark() { // {{{
    i64 s = 0;
    n = GetN();
    for (i64 i = 0; i < n; i++)
        s = s + GetElement(i) * 123ll % 12321ll;
} // }}}
#ifdef WITHOUT_RPA // {{{ message
int NumberOfNodes() { return 4; }

int MyNodeId() { return 0; }

void PutChar(int target, char value);

void PutInt(int target, int value);

void PutLL(int target, long long value);

void Send(int target);

int Receive(int source);

char GetChar(int source);

int GetInt(int source);

long long GetLL(int source);

#endif // }}}

// {{{ comm
void send(i64 t, i64 v) {
#ifdef WITHOUT_RPA
    print("would send to"); print(t); print("value"); println(v);
#else
    dprint(node_id); dprint("sending to"); dprint(t); dprint("value"); dprintln(v);
    PutLL(t, v);
    Send(t);
#endif
}
void send(i64 t, vi v) {
#ifdef WITHOUT_RPA
    print("would send to"); print(t); print("value"); println(v);
#else
    dprint(node_id); dprint("sending to"); dprint(t); dprint("value"); dprintln(v);
    for (auto e : v) PutLL(t, e);
    Send(t);
#endif
}
void send(i64 t, pair<i64, i64> v) {
#ifdef WITHOUT_RPA
    print("would send to"); print(t); print("value"); println(v);
#else
    dprint(node_id); dprint("sending to"); dprint(t); dprint("value"); dprintln(v);
    PutLL(t, v.first);
    PutLL(t, v.second);
    Send(t);
#endif
}
i64 retrieve_i64(i64 t, bool receive = true) {
#ifdef WITHOUT_RPA
    print("would retrieve from"); println(t); print("with cereive"); println(receive);
    return t;
#else
    dprint(node_id); dprint("retrieving from"); dprintln(t);
    if (receive)
        Receive(t);
    i64 const res = GetLL(t);
    dprint(node_id); dprint("retrieved from"); dprint(t); dprint("value"); dprintln(res);
    return res;
#endif
}
pair<i64, i64> retrieve_pii(i64 t) {
    i64 a = retrieve_i64(t);
    auto res = pair<i64, i64>{a, retrieve_i64(t, false)};
    dprint(node_id); dprint("retrieved from"); dprint(t); dprint("value"); dprintln(res);
    return res;
}
void retrieve(i64 t, vi & res, i64 c) {
//    dprint(node_id); dprint("retrieving from"); dprint(t); dprint(c); dprintln("values");
    i64 const old_size = len(res);
    res.resize(len(res) + c);
    Receive(t);
    for (i64 i = old_size; i < len(res); i++) {
        res[i] = retrieve_i64(t, false);
    }
    dprint(node_id); dprint("retrieved from"); dprint(t); dprint(c); dprint("values from"); dprintln(res);
}
vi retrieve_vi(i64 t, i64 c) {
    vi res;
    retrieve(t, res, c);
    return res;
}
 // }}}
vi elements;
pair<i64, i64> my_split_;

void init_element_cache() {
    my_split_ = my_split();
    elements.resize(my_split_.second - my_split_.first + 1);
    for (i64 i = my_split_.first; i <= my_split_.second; ++i)
        elements[i - my_split_.first] = GetElement(i);
}
i64 get_element(i64 k) {
    if (elements.empty())
        return GetElement(k);
    if (k < my_split_.first || k > my_split_.second)
        return GetElement(k);
    return elements[k - my_split_.first];
}

vi node_pos_stats;
void calc_node_pos_stats() {
    node_pos_stats.clear();
    elements.clear();
    pair<i64, i64> i_interval = my_split();
    vi counts(v_max + 1, 0);
    for (i64 i = i_interval.first; i <= i_interval.second; ++i) {
        elements.push_back(get_element(i));
        ++counts[elements.back()];
    }
    i64 c = 0;
    vi const limits = split_range(0, i_interval.second - i_interval.first + 1, nodes_cnt);
    dprint(node_id); dprint("calcs node pos stats with interval"); dprint(i_interval);
    dprint("limits"); dprint(limits);
    dprint("counts"); dprintln(counts);
    i64 limit_i = 0;
    for (i64 v = 1; v <= v_max; v++) {
        c += counts[v];
        while (limit_i < len(limits) && c >= limits[limit_i]) {
            node_pos_stats.push_back(v);
            ++limit_i;
        }
    }
}
vi tree;
i64 tree_sum;
vi tree_stage;
void add_to_tree(i64 e) {
    tree_stage.push_back(e);
}
i64 get_from_tree(i64 e) {
    i64 res = 0;
    do {
        res += tree[e];
        e -= e & (~(e - 1));
    } while (e > 0);
    return tree_sum - res;
}
void flush_tree() {
    for (auto e : tree_stage) {
        do {
            ++tree[e];
            e += e & (~(e - 1));
        } while (e <= v_max);
    }
    tree_sum += len(tree_stage);
    tree_stage.clear();
}
vi counts_in_row;
i64 calc_for_row_column(pair<i64, i64> value_interval, pair<i64, i64> index_interval, bool count = false, bool dont_count_in_index_interval = false) {
    i64 res = 0;
    i64 value_count = 0;
    tree = vi(v_max + 1, 0);
    tree_sum = 0;
    tree_stage.clear();
    i64 col_num = 0;
    if (count)
        counts_in_row.resize(nodes_cnt);
    auto const count_range = split_range(0, n, nodes_cnt);
    for (i64 i = index_interval.first; i <= index_interval.second; ++i) {
        i64 const e = get_element(i);
        //println(e);
        if (count_range[col_num] == i) {
            ++col_num;
            flush_tree();
        }
        if (e < value_interval.first || e > value_interval.second)
            continue;
        if (count) {
            ++counts_in_row[col_num];
        }
        ++value_count;
        if (value_interval.first != value_interval.second) {
            res += get_from_tree(e);
            add_to_tree(e);
            if (!dont_count_in_index_interval)
                flush_tree();
        }
    }
    flush_tree();
    if (value_interval.first == value_interval.second)
        res = 0;
    dprint(node_id); dprint("res for values"); dprint(value_interval); dprint("indexes"); dprint(index_interval); dprint("is"); dprintln(res);
    return res;
}

pair<i64, i64> row_assignment;
i64 node_result;
void calc_results_and_counts() {
    node_result += calc_for_row_column({0, v_max}, my_split());
    node_result += calc_for_row_column(row_assignment, max_split(), true, true);
    dprint(node_id); dprint("result"); dprint(node_result); dprint("counts"); dprintln(counts_in_row);
}

void worker_workflow() {
    init_element_cache();
    calc_node_pos_stats();
    send(0, node_pos_stats);
    row_assignment = retrieve_pii(0);
    calc_results_and_counts();
    send(0, node_result);
    send(0, counts_in_row);
}

vi pos_stats_from_nodes;
void root_get_pos_stats_from_nodes() {
    dprintln("root_get_pos_stats_from_nodes starts");
    pos_stats_from_nodes = node_pos_stats;
    for (i64 i = 1; i < nodes_cnt; i++)
        retrieve(i, pos_stats_from_nodes, nodes_cnt);
    dprintln("root_get_pos_stats_from_nodes succeeded");
}

vector<pair<i64, i64>> row_assignments;
void calc_row_assignments_from_pos_stats() {
    row_assignments = {};
    sort(pos_stats_from_nodes.begin(), pos_stats_from_nodes.end());
    i64 prev = 0;
    for (i64 i = 0; i < nodes_cnt; ++i) {
        i64 const cur = pos_stats_from_nodes[(i + 1) * nodes_cnt - 1];
        i64 const next = i + 1 < nodes_cnt ? pos_stats_from_nodes[(i + 2) * nodes_cnt - 1] : 0;
        if (prev != cur && cur == next) {
            row_assignments.push_back(make_pair(prev + 1, cur - 1));
            row_assignments.push_back(make_pair(cur, cur));
        } else {
            if (prev != cur)
                row_assignments.push_back(make_pair(prev + 1, cur));
        }
        prev = cur;
    }
    while (len(row_assignments) < nodes_cnt)
        row_assignments.push_back({0, 0});
    dprint("row assignments"); dprintln(row_assignments);
}


i64 result;
vvi count_matrix;

void root_get_results_from_nodes() {
    result = node_result;
    count_matrix = {counts_in_row};
    for (i64 i = 1; i < nodes_cnt; i++) {
        result += retrieve_i64(i);
        count_matrix.push_back(retrieve_vi(i, nodes_cnt));
    }
    reverse(count_matrix.begin(), count_matrix.end());
}

vvi counts;
void aggregate_result_for_matrix() {
    counts = vvi(nodes_cnt + 1, vi(nodes_cnt + 1, 0));
    dprintln(result);
    dprintln(count_matrix);
    for (i64 i = 0; i < nodes_cnt; ++i) {
        for (i64 j = 0; j < nodes_cnt; ++j) {
            result += counts[i][j] * count_matrix[i][j];
            counts[i + 1][j + 1] = count_matrix[i][j] + counts[i][j + 1] + counts[i + 1][j] - counts[i][j];
        }
    }
    dprintln(result);
//    for (auto c : counts) println(c);
}
void root_workflow() {
    dprint("root"); dprint("starts work with nodes"); dprint(nodes_cnt); dprint("and n"); dprintln(n);
    init_element_cache();
    calc_node_pos_stats();
    root_get_pos_stats_from_nodes();
    calc_row_assignments_from_pos_stats();
    for (i64 i = 1; i < nodes_cnt; i++)
        send(i, row_assignments[i]);
    row_assignment = row_assignments[0];
    calc_results_and_counts();
    root_get_results_from_nodes();
    aggregate_result_for_matrix();
}

void go() {
    node_id = MyNodeId();
    nodes_cnt = NumberOfNodes();
    n = GetN();
    if (n <= nodes_cnt * nodes_cnt) {
        if (node_id == 0)
            println(calc_for_row_column(make_pair(0, v_max), make_pair(0, n - 1)));
//        nodes_cnt = 1;
//        if (node_id != 0)
        return;
    }
    if (node_id == 0) {
        root_workflow();
        println(result);
    } else
        worker_workflow();
}
// {{{ tests
void test_aggregate() {
    nodes_cnt = 5;
    result = 0;
    count_matrix = {
        {2, 3, 2, 4, 5},
        {10, 10, 20, 30, 10},
        {100, 100, 100, 200, 100},
        {1000, 1000, 1000, 1000, 1000},
        {10000, 10000, 10000, 10000, 10000}
    };
    aggregate_result_for_matrix();
    println(result);
    nodes_cnt = 3;
    result = 0;
    count_matrix = {
        {3, 1, 3},
        {2, 4, 6},
        {1, 1, 1}
    };
    aggregate_result_for_matrix();
    println(result);
}

#ifdef MY_COMPUTER2

void test_node_pos_stats() {
//    nodes_cnt = 3;
//    node_id = 0;
//    mock_data = {1, 2, 3, 3, 3, 3, 3, 8, 9};
//    mock_data.resize(len(mock_data) * nodes_cnt);
//    n = GetN();
//    calc_node_pos_stats();
//    println(node_pos_stats);

    nodes_cnt = 1;
    mock_data = {1, 2, 3, 4, 5};
    n = GetN();
    calc_node_pos_stats();
    println(node_pos_stats);
}

void test_counts() {
    mock_data = {100, 5, 2, 1000, 1, 4, 4};
    nodes_cnt = 3;
    n = 9;
    mock_data.resize(n);
    calc_for_row_column({1, 2000}, {0, 8}, true);
    println(split_range(0, n, nodes_cnt));
}

void test_calc_for_row_column() {
    mock_data = {100, 5, 2, 1000, 1, 4, 4, 3, 1};
    println(calc_for_row_column({2, 200}, {1, 7}));
    test_counts();
}


void tests_calc_row_assignments_from_pos_stats() {
//    nodes_cnt = 2;
//    pos_stats_from_nodes = {2, 2, 2, 2};
//    calc_row_assignments_from_pos_stats();
//    println(row_assignments);
//    nodes_cnt = 4;
//    pos_stats_from_nodes = {1, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 13};
//    calc_row_assignments_from_pos_stats();
//    println(row_assignments);
    nodes_cnt = 1;
    pos_stats_from_nodes = {13};
    calc_row_assignments_from_pos_stats();
    println(row_assignments);
}
void test_tree() {
    tree = vi(v_max + 1, 0);
    add_to_tree(2);
    add_to_tree(5);
    add_to_tree(7);
    println(get_from_tree(1));
    println(get_from_tree(2));
    println(get_from_tree(3));
    println(get_from_tree(6));
    println(get_from_tree(9));
}
 // }}}
#endif

int main () { // {{{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    go();
} //