답안 #723406

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
723406 2023-04-13T17:47:57 Z drdilyor Boarding Passes (BOI22_passes) C++17
100 / 100
1256 ms 377008 KB
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define time(code) {auto _s = chrono::high_resolution_clock::now(); code;cerr << (chrono::high_resolution_clock::now() - _s).count() / 1e9 << '\n';}
 
inline ll exp_inv(ll x) {
    return x * (x-1);
}
 
int main() {
    cin.tie(0)->sync_with_stdio(0);
    char a = 'A';
    string s; cin >> s;
    const int G = 15, N = 1e5;
    int n = s.size();
    if (n == 1) {
        cout << "0\n";
        return 0;
    }

    ll suml[G][G][N];
    ll sumr[G][G][N];
    ll cr[G][N];
    ll cl[G][N];
    int cnt[G]{};
    vector ix(G, vector<int>());

    time(({
        for (int c1 = 0; c1 < G; c1++) {
            for (int c2 = 0; c2 < G; c2++) {
                ll res = 0, cur = 0;
                for (int i = 0; i < n; i++) {
                    if (s[i] == c1+a)
                        res += cur;
                    else if (s[i] == c2+a)
                        cur++;
                    suml[c1][c2][i] = res;
                }
            }
        }
        for (int c1 = 0; c1 < G; c1++) {
            for (int c2 = 0; c2 < G; c2++) {
                ll res = 0, cur = 0;
                for (int i = n-1; i >= 0; i --) {
                    if (s[i] == c1+a)
                        res += cur;
                    else if (s[i] == c2+a)
                        cur++;
                    sumr[c1][c2][i] = res;
                }
            }
        }
        for (int j = 0; j < G; j++) {
            int c = 0;
            for (int i = 0; i < n;i ++) {
                if (s[i] == j+a)
                    c++;
                cl[j][i] = c;
            }
        }
        for (int j = 0; j < G; j++) {
            int c = 0;
            for (int i = n-1; i >= 0; i--) {
                if (s[i] == j+a)
                    c++;
                cr[j][i] = c;
            }
        }
        for (int i = 0; i < n; i++)
            cnt[s[i] - a]++;
        for (int i = 0; i < G; i++)
            ix[i].reserve(cnt[i]);
        for (int i = 0; i < n ;i++) 
            ix[s[i] - a].push_back(i);
    }));


    ll memo[1<<G];
    memo[(1<<G)-1] = 0;
    for (int used = (1<<G)-1-1; used >= 0; used--) {
        ll& res = memo[used];
        res = 1e18;
        for (int i = 0 ;i < G; i++) {
            if (used&1<<i) continue;

            auto f = [&](int i, int j) {
                ll sum = 0;
                for (int c2 = 0; c2 < G; c2++)
                    if (j) sum += (used>>c2&1) * suml[i][c2][j-1];
                for (int c2 = 0; c2 < G; c2++)
                    if (j<n) sum += (used>>c2&1) * sumr[i][c2][j];
                return sum * 4 + (j < n ? exp_inv(cr[i][j]) : 0) + (j ? exp_inv(cl[i][j-1]) : 0);
            };

            int l = -1, r = (int)ix[i].size()-2;
            while (l < r-1) {
                int m = (l+r) / 2;
                ll a = f(i, ix[i][m]), b = f(i, ix[i][m+1]);
                if (a < b) r = m;
                else l = m;
            }
 
            ll cur = min(f(i, 0), f(i, n));;
            for (int j = max(l-1, 0); j < min((int)ix[i].size(), 2 + max(0, r)); j++) {
                cur = min(cur, f(i, ix[i][j]));
            }
            res = min(res, cur + memo[used|1<<i]);
        }
    };
    ll ans;
    ans = memo[0];
 
    cout << ans / 4;
    if (ans%4 == 1) cout << ".25";
    if (ans%4 == 2) cout << ".5";
    if (ans%4== 3) cout << ".75";
    cout << endl;
}

# 결과 실행 시간 메모리 Grader output
1 Correct 169 ms 376276 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 138 ms 376216 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 174 ms 376280 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 152 ms 376248 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 161 ms 376288 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 220 ms 376740 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 220 ms 376888 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 229 ms 376888 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 234 ms 376908 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
# 결과 실행 시간 메모리 Grader output
1 Correct 169 ms 376276 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 164 ms 376384 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 244 ms 376284 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 193 ms 376196 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 162 ms 376380 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 155 ms 376184 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 215 ms 376324 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 183 ms 376316 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 176 ms 376292 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 184 ms 376288 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 173 ms 376248 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 175 ms 376236 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 183 ms 376288 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
14 Correct 193 ms 376224 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
15 Correct 182 ms 376260 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 178 ms 376312 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
17 Correct 184 ms 376288 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
# 결과 실행 시간 메모리 Grader output
1 Correct 169 ms 376276 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
2 Correct 164 ms 376384 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
3 Correct 244 ms 376284 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
4 Correct 193 ms 376196 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
5 Correct 162 ms 376380 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
6 Correct 155 ms 376184 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
7 Correct 215 ms 376324 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
8 Correct 183 ms 376316 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
9 Correct 176 ms 376292 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
10 Correct 184 ms 376288 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
11 Correct 173 ms 376248 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
12 Correct 175 ms 376236 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
13 Correct 183 ms 376288 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
14 Correct 193 ms 376224 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
15 Correct 182 ms 376260 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
16 Correct 178 ms 376312 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
17 Correct 184 ms 376288 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
18 Correct 156 ms 376192 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
19 Correct 165 ms 376288 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
20 Correct 208 ms 376324 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
21 Correct 194 ms 376288 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
22 Correct 182 ms 376268 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
23 Correct 163 ms 376240 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
24 Correct 210 ms 376268 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
25 Correct 172 ms 376184 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
26 Correct 190 ms 376268 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
27 Correct 182 ms 376312 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
28 Correct 174 ms 376288 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
29 Correct 180 ms 376224 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
30 Correct 208 ms 376268 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
31 Correct 184 ms 376272 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
32 Correct 197 ms 376388 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
33 Correct 186 ms 376272 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
34 Correct 187 ms 376268 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
35 Correct 171 ms 376356 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
36 Correct 174 ms 376268 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
37 Correct 461 ms 376348 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
38 Correct 353 ms 376348 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
39 Correct 183 ms 376432 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
40 Correct 350 ms 376396 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
41 Correct 391 ms 376396 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
42 Correct 400 ms 376348 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
43 Correct 437 ms 376348 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
44 Correct 417 ms 376344 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
45 Correct 412 ms 376352 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
46 Correct 403 ms 376432 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
# 결과 실행 시간 메모리 Grader output
1 Correct 169 ms 376276 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
2 Correct 138 ms 376216 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
3 Correct 174 ms 376280 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
4 Correct 152 ms 376248 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
5 Correct 161 ms 376288 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
6 Correct 220 ms 376740 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
7 Correct 220 ms 376888 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
8 Correct 229 ms 376888 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
9 Correct 234 ms 376908 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
10 Correct 169 ms 376276 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
11 Correct 164 ms 376384 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
12 Correct 244 ms 376284 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
13 Correct 193 ms 376196 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
14 Correct 162 ms 376380 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
15 Correct 155 ms 376184 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
16 Correct 215 ms 376324 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
17 Correct 183 ms 376316 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
18 Correct 176 ms 376292 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
19 Correct 184 ms 376288 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
20 Correct 173 ms 376248 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
21 Correct 175 ms 376236 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
22 Correct 183 ms 376288 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
23 Correct 193 ms 376224 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
24 Correct 182 ms 376260 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
25 Correct 178 ms 376312 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
26 Correct 184 ms 376288 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
27 Correct 156 ms 376192 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
28 Correct 165 ms 376288 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
29 Correct 208 ms 376324 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
30 Correct 194 ms 376288 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
31 Correct 182 ms 376268 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
32 Correct 163 ms 376240 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
33 Correct 210 ms 376268 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
34 Correct 172 ms 376184 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
35 Correct 190 ms 376268 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
36 Correct 182 ms 376312 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
37 Correct 174 ms 376288 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
38 Correct 180 ms 376224 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
39 Correct 208 ms 376268 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
40 Correct 184 ms 376272 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
41 Correct 197 ms 376388 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
42 Correct 186 ms 376272 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
43 Correct 187 ms 376268 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
44 Correct 171 ms 376356 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
45 Correct 174 ms 376268 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
46 Correct 461 ms 376348 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
47 Correct 353 ms 376348 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
48 Correct 183 ms 376432 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
49 Correct 350 ms 376396 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
50 Correct 391 ms 376396 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
51 Correct 400 ms 376348 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
52 Correct 437 ms 376348 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
53 Correct 417 ms 376344 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
54 Correct 412 ms 376352 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
55 Correct 403 ms 376432 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
56 Correct 177 ms 376184 KB found '7.5000000000', expected '7.5000000000', error '0.0000000000'
57 Correct 175 ms 376272 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
58 Correct 171 ms 376212 KB found '100800.5000000000', expected '100800.5000000000', error '0.0000000000'
59 Correct 138 ms 376268 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
60 Correct 154 ms 376276 KB found '0.0000000000', expected '0.0000000000', error '-0.0000000000'
61 Correct 151 ms 376292 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
62 Correct 169 ms 376268 KB found '124002.0000000000', expected '124002.0000000000', error '0.0000000000'
63 Correct 214 ms 376708 KB found '772893586.0000000000', expected '772893586.0000000000', error '0.0000000000'
64 Correct 222 ms 376772 KB found '1100977812.5000000000', expected '1100977812.5000000000', error '0.0000000000'
65 Correct 225 ms 376904 KB found '1249950000.5000000000', expected '1249950000.5000000000', error '0.0000000000'
66 Correct 233 ms 376896 KB found '1249975000.0000000000', expected '1249975000.0000000000', error '0.0000000000'
67 Correct 158 ms 376172 KB found '1.0000000000', expected '1.0000000000', error '0.0000000000'
68 Correct 169 ms 376252 KB found '1225.0000000000', expected '1225.0000000000', error '0.0000000000'
69 Correct 201 ms 376184 KB found '1023.0000000000', expected '1023.0000000000', error '0.0000000000'
70 Correct 202 ms 376296 KB found '294.0000000000', expected '294.0000000000', error '0.0000000000'
71 Correct 165 ms 376292 KB found '1087.0000000000', expected '1087.0000000000', error '0.0000000000'
72 Correct 157 ms 376184 KB found '1.5000000000', expected '1.5000000000', error '0.0000000000'
73 Correct 203 ms 376288 KB found '703.0000000000', expected '703.0000000000', error '0.0000000000'
74 Correct 177 ms 376268 KB found '55.5000000000', expected '55.5000000000', error '0.0000000000'
75 Correct 178 ms 376196 KB found '56.0000000000', expected '56.0000000000', error '0.0000000000'
76 Correct 202 ms 376224 KB found '45.0000000000', expected '45.0000000000', error '0.0000000000'
77 Correct 173 ms 376228 KB found '66.5000000000', expected '66.5000000000', error '0.0000000000'
78 Correct 179 ms 376268 KB found '67.0000000000', expected '67.0000000000', error '0.0000000000'
79 Correct 200 ms 376472 KB found '66.0000000000', expected '66.0000000000', error '0.0000000000'
80 Correct 182 ms 376172 KB found '47.0000000000', expected '47.0000000000', error '0.0000000000'
81 Correct 178 ms 376192 KB found '50.0000000000', expected '50.0000000000', error '0.0000000000'
82 Correct 179 ms 376292 KB found '49.0000000000', expected '49.0000000000', error '0.0000000000'
83 Correct 175 ms 376220 KB found '57.0000000000', expected '57.0000000000', error '0.0000000000'
84 Correct 179 ms 376268 KB found '12497500.0000000000', expected '12497500.0000000000', error '0.0000000000'
85 Correct 174 ms 376288 KB found '12495000.5000000000', expected '12495000.5000000000', error '0.0000000000'
86 Correct 472 ms 376316 KB found '12223392.0000000000', expected '12223392.0000000000', error '0.0000000000'
87 Correct 316 ms 376344 KB found '2372500.0000000000', expected '2372500.0000000000', error '0.0000000000'
88 Correct 189 ms 376352 KB found '12475017.5000000000', expected '12475017.5000000000', error '0.0000000000'
89 Correct 374 ms 376328 KB found '10655706.0000000000', expected '10655706.0000000000', error '0.0000000000'
90 Correct 425 ms 376340 KB found '11977895.5000000000', expected '11977895.5000000000', error '0.0000000000'
91 Correct 386 ms 376344 KB found '11977865.0000000000', expected '11977865.0000000000', error '0.0000000000'
92 Correct 421 ms 376352 KB found '11977907.5000000000', expected '11977907.5000000000', error '0.0000000000'
93 Correct 402 ms 376252 KB found '11977808.0000000000', expected '11977808.0000000000', error '0.0000000000'
94 Correct 389 ms 376272 KB found '11977791.0000000000', expected '11977791.0000000000', error '0.0000000000'
95 Correct 421 ms 376364 KB found '11977871.5000000000', expected '11977871.5000000000', error '0.0000000000'
96 Correct 1256 ms 376800 KB found '1239972790.0000000000', expected '1239972790.0000000000', error '0.0000000000'
97 Correct 193 ms 376252 KB found '128.0000000000', expected '128.0000000000', error '0.0000000000'
98 Correct 708 ms 376796 KB found '161053893.0000000000', expected '161053893.0000000000', error '0.0000000000'
99 Correct 259 ms 376900 KB found '1249625032.0000000000', expected '1249625032.0000000000', error '0.0000000000'
100 Correct 169 ms 376268 KB found '10.5000000000', expected '10.5000000000', error '0.0000000000'
101 Correct 974 ms 376808 KB found '1095334900.0000000000', expected '1095334900.0000000000', error '0.0000000000'
102 Correct 1191 ms 376788 KB found '1249723731.0000000000', expected '1249723731.0000000000', error '0.0000000000'
103 Correct 1190 ms 376992 KB found '1239994164.5000000000', expected '1239994164.5000000000', error '0.0000000000'
104 Correct 1187 ms 377008 KB found '1239994234.5000000000', expected '1239994234.5000000000', error '0.0000000000'
105 Correct 1110 ms 376904 KB found '1239994121.0000000000', expected '1239994121.0000000000', error '0.0000000000'
106 Correct 1124 ms 376960 KB found '1239994009.0000000000', expected '1239994009.0000000000', error '0.0000000000'
107 Correct 1114 ms 376880 KB found '1239993860.5000000000', expected '1239993860.5000000000', error '0.0000000000'
108 Correct 1138 ms 376888 KB found '1237107336.5000000000', expected '1237107336.5000000000', error '0.0000000000'
109 Correct 1124 ms 376940 KB found '1239994062.5000000000', expected '1239994062.5000000000', error '0.0000000000'