Submission #1018885

# Submission time Handle Problem Language Result Execution time Memory
1018885 2024-07-10T10:38:32 Z socpite Traffic (IOI10_traffic) C++14
100 / 100
647 ms 178512 KB
#include "traffic.h"
#include <bits/stdc++.h>
using namespace std;

const int maxn = 1e6+5;
const long long INF = 1e18;

vector<int> g[maxn];
long long sz[maxn], mx[maxn];

int dfs(int x, int p, long long tot){
   int re = -1;
   mx[x] = 0;

   for(auto v: g[x]){
      if(v == p)continue;
      int tmp = dfs(v, x, tot);
      sz[x] += sz[v];
      mx[x] = max(mx[x], sz[v]);

      if(re == -1 || mx[tmp] < mx[re])re = tmp;      
   }
   mx[x] = max(mx[x], tot - sz[x]);
   if(re == -1 || mx[x] < mx[re])re = x;
   return re;
}

int LocateCentre(int N, int pp[], int S[], int D[]) {
   long long sum = 0;
   for(int i = 0; i < N; i++){
      g[i].clear();
      sz[i] = pp[i];
      sum += pp[i];
   }
   for(int i = 0; i < N-1; i++){
      g[S[i]].push_back(D[i]);
      g[D[i]].push_back(S[i]);
   }
   return dfs(0, -1, sum);
}
# Verdict Execution time Memory Grader output
1 Correct 10 ms 23896 KB Output is correct
2 Correct 10 ms 23900 KB Output is correct
3 Correct 9 ms 23900 KB Output is correct
4 Correct 10 ms 23900 KB Output is correct
5 Correct 9 ms 23932 KB Output is correct
6 Correct 10 ms 23896 KB Output is correct
7 Correct 10 ms 23828 KB Output is correct
8 Correct 10 ms 23900 KB Output is correct
9 Correct 10 ms 23940 KB Output is correct
10 Correct 12 ms 23900 KB Output is correct
11 Correct 10 ms 23900 KB Output is correct
12 Correct 10 ms 23900 KB Output is correct
13 Correct 10 ms 23896 KB Output is correct
14 Correct 11 ms 23900 KB Output is correct
15 Correct 11 ms 23900 KB Output is correct
16 Correct 10 ms 23888 KB Output is correct
17 Correct 10 ms 23896 KB Output is correct
18 Correct 10 ms 23956 KB Output is correct
19 Correct 9 ms 23944 KB Output is correct
20 Correct 10 ms 23900 KB Output is correct
21 Correct 10 ms 23796 KB Output is correct
22 Correct 10 ms 23896 KB Output is correct
23 Correct 10 ms 23900 KB Output is correct
24 Correct 9 ms 23908 KB Output is correct
25 Correct 10 ms 23896 KB Output is correct
26 Correct 10 ms 23900 KB Output is correct
27 Correct 10 ms 23900 KB Output is correct
28 Correct 10 ms 23940 KB Output is correct
29 Correct 10 ms 23896 KB Output is correct
30 Correct 9 ms 23784 KB Output is correct
31 Correct 10 ms 23900 KB Output is correct
32 Correct 10 ms 23816 KB Output is correct
33 Correct 10 ms 23984 KB Output is correct
34 Correct 13 ms 23896 KB Output is correct
35 Correct 10 ms 23900 KB Output is correct
36 Correct 10 ms 23892 KB Output is correct
37 Correct 10 ms 23900 KB Output is correct
38 Correct 12 ms 23900 KB Output is correct
39 Correct 10 ms 23900 KB Output is correct
40 Correct 10 ms 23900 KB Output is correct
41 Correct 10 ms 23900 KB Output is correct
42 Correct 10 ms 24020 KB Output is correct
43 Correct 10 ms 23896 KB Output is correct
44 Correct 12 ms 23900 KB Output is correct
45 Correct 10 ms 23900 KB Output is correct
46 Correct 10 ms 23896 KB Output is correct
47 Correct 10 ms 23944 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 10 ms 23896 KB Output is correct
2 Correct 10 ms 23900 KB Output is correct
3 Correct 9 ms 23900 KB Output is correct
4 Correct 10 ms 23900 KB Output is correct
5 Correct 9 ms 23932 KB Output is correct
6 Correct 10 ms 23896 KB Output is correct
7 Correct 10 ms 23828 KB Output is correct
8 Correct 10 ms 23900 KB Output is correct
9 Correct 10 ms 23940 KB Output is correct
10 Correct 12 ms 23900 KB Output is correct
11 Correct 10 ms 23900 KB Output is correct
12 Correct 10 ms 23900 KB Output is correct
13 Correct 10 ms 23896 KB Output is correct
14 Correct 11 ms 23900 KB Output is correct
15 Correct 11 ms 23900 KB Output is correct
16 Correct 10 ms 23888 KB Output is correct
17 Correct 10 ms 23896 KB Output is correct
18 Correct 10 ms 23956 KB Output is correct
19 Correct 9 ms 23944 KB Output is correct
20 Correct 10 ms 23900 KB Output is correct
21 Correct 10 ms 23796 KB Output is correct
22 Correct 10 ms 23896 KB Output is correct
23 Correct 10 ms 23900 KB Output is correct
24 Correct 9 ms 23908 KB Output is correct
25 Correct 10 ms 23896 KB Output is correct
26 Correct 10 ms 23900 KB Output is correct
27 Correct 10 ms 23900 KB Output is correct
28 Correct 10 ms 23940 KB Output is correct
29 Correct 10 ms 23896 KB Output is correct
30 Correct 9 ms 23784 KB Output is correct
31 Correct 10 ms 23900 KB Output is correct
32 Correct 10 ms 23816 KB Output is correct
33 Correct 10 ms 23984 KB Output is correct
34 Correct 13 ms 23896 KB Output is correct
35 Correct 10 ms 23900 KB Output is correct
36 Correct 10 ms 23892 KB Output is correct
37 Correct 10 ms 23900 KB Output is correct
38 Correct 12 ms 23900 KB Output is correct
39 Correct 10 ms 23900 KB Output is correct
40 Correct 10 ms 23900 KB Output is correct
41 Correct 10 ms 23900 KB Output is correct
42 Correct 10 ms 24020 KB Output is correct
43 Correct 10 ms 23896 KB Output is correct
44 Correct 12 ms 23900 KB Output is correct
45 Correct 10 ms 23900 KB Output is correct
46 Correct 10 ms 23896 KB Output is correct
47 Correct 10 ms 23944 KB Output is correct
48 Correct 10 ms 23896 KB Output is correct
49 Correct 10 ms 23964 KB Output is correct
50 Correct 10 ms 23968 KB Output is correct
51 Correct 10 ms 23952 KB Output is correct
52 Correct 10 ms 23900 KB Output is correct
53 Correct 9 ms 23936 KB Output is correct
54 Correct 10 ms 23844 KB Output is correct
55 Correct 10 ms 23900 KB Output is correct
56 Correct 9 ms 23900 KB Output is correct
57 Correct 10 ms 23956 KB Output is correct
58 Correct 10 ms 23900 KB Output is correct
59 Correct 11 ms 23900 KB Output is correct
60 Correct 13 ms 23944 KB Output is correct
61 Correct 10 ms 23900 KB Output is correct
62 Correct 9 ms 23900 KB Output is correct
63 Correct 10 ms 23900 KB Output is correct
64 Correct 9 ms 23900 KB Output is correct
65 Correct 10 ms 23968 KB Output is correct
66 Correct 9 ms 23800 KB Output is correct
67 Correct 9 ms 23900 KB Output is correct
68 Correct 27 ms 31580 KB Output is correct
69 Correct 57 ms 39212 KB Output is correct
70 Correct 11 ms 24152 KB Output is correct
71 Correct 59 ms 46932 KB Output is correct
72 Correct 71 ms 54788 KB Output is correct
73 Correct 78 ms 62548 KB Output is correct
74 Correct 95 ms 70204 KB Output is correct
75 Correct 108 ms 77904 KB Output is correct
76 Correct 124 ms 85840 KB Output is correct
77 Correct 140 ms 93524 KB Output is correct
78 Correct 155 ms 101112 KB Output is correct
79 Correct 164 ms 108880 KB Output is correct
80 Correct 176 ms 116620 KB Output is correct
81 Correct 10 ms 23900 KB Output is correct
82 Correct 203 ms 124480 KB Output is correct
83 Correct 206 ms 132096 KB Output is correct
84 Correct 223 ms 139952 KB Output is correct
85 Correct 240 ms 147792 KB Output is correct
86 Correct 253 ms 155472 KB Output is correct
87 Correct 270 ms 163152 KB Output is correct
88 Correct 284 ms 170832 KB Output is correct
89 Correct 301 ms 178512 KB Output is correct
90 Correct 11 ms 23896 KB Output is correct
91 Correct 9 ms 23900 KB Output is correct
92 Correct 9 ms 23900 KB Output is correct
93 Correct 9 ms 23912 KB Output is correct
94 Correct 9 ms 23900 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 10 ms 23896 KB Output is correct
2 Correct 10 ms 23900 KB Output is correct
3 Correct 9 ms 23900 KB Output is correct
4 Correct 10 ms 23900 KB Output is correct
5 Correct 9 ms 23932 KB Output is correct
6 Correct 10 ms 23896 KB Output is correct
7 Correct 10 ms 23828 KB Output is correct
8 Correct 10 ms 23900 KB Output is correct
9 Correct 10 ms 23940 KB Output is correct
10 Correct 12 ms 23900 KB Output is correct
11 Correct 10 ms 23900 KB Output is correct
12 Correct 10 ms 23900 KB Output is correct
13 Correct 10 ms 23896 KB Output is correct
14 Correct 11 ms 23900 KB Output is correct
15 Correct 11 ms 23900 KB Output is correct
16 Correct 10 ms 23888 KB Output is correct
17 Correct 10 ms 23896 KB Output is correct
18 Correct 10 ms 23956 KB Output is correct
19 Correct 9 ms 23944 KB Output is correct
20 Correct 10 ms 23900 KB Output is correct
21 Correct 10 ms 23796 KB Output is correct
22 Correct 10 ms 23896 KB Output is correct
23 Correct 10 ms 23900 KB Output is correct
24 Correct 9 ms 23908 KB Output is correct
25 Correct 10 ms 23896 KB Output is correct
26 Correct 10 ms 23900 KB Output is correct
27 Correct 10 ms 23900 KB Output is correct
28 Correct 10 ms 23940 KB Output is correct
29 Correct 10 ms 23896 KB Output is correct
30 Correct 9 ms 23784 KB Output is correct
31 Correct 10 ms 23900 KB Output is correct
32 Correct 10 ms 23816 KB Output is correct
33 Correct 10 ms 23984 KB Output is correct
34 Correct 13 ms 23896 KB Output is correct
35 Correct 10 ms 23900 KB Output is correct
36 Correct 10 ms 23892 KB Output is correct
37 Correct 10 ms 23900 KB Output is correct
38 Correct 12 ms 23900 KB Output is correct
39 Correct 10 ms 23900 KB Output is correct
40 Correct 10 ms 23900 KB Output is correct
41 Correct 10 ms 23900 KB Output is correct
42 Correct 10 ms 24020 KB Output is correct
43 Correct 10 ms 23896 KB Output is correct
44 Correct 12 ms 23900 KB Output is correct
45 Correct 10 ms 23900 KB Output is correct
46 Correct 10 ms 23896 KB Output is correct
47 Correct 10 ms 23944 KB Output is correct
48 Correct 9 ms 23900 KB Output is correct
49 Correct 9 ms 23900 KB Output is correct
50 Correct 9 ms 23900 KB Output is correct
51 Correct 9 ms 23932 KB Output is correct
52 Correct 10 ms 23900 KB Output is correct
53 Correct 10 ms 23944 KB Output is correct
54 Correct 12 ms 23940 KB Output is correct
55 Correct 11 ms 23900 KB Output is correct
56 Correct 10 ms 23900 KB Output is correct
57 Correct 9 ms 23896 KB Output is correct
58 Correct 9 ms 23900 KB Output is correct
59 Correct 10 ms 23900 KB Output is correct
60 Correct 9 ms 23900 KB Output is correct
61 Correct 9 ms 23900 KB Output is correct
62 Correct 9 ms 23900 KB Output is correct
63 Correct 9 ms 23900 KB Output is correct
64 Correct 9 ms 23796 KB Output is correct
65 Correct 12 ms 23900 KB Output is correct
66 Correct 10 ms 23952 KB Output is correct
67 Correct 10 ms 23900 KB Output is correct
68 Correct 9 ms 23828 KB Output is correct
69 Correct 9 ms 23900 KB Output is correct
70 Correct 10 ms 23708 KB Output is correct
71 Correct 9 ms 23900 KB Output is correct
72 Correct 13 ms 23924 KB Output is correct
73 Correct 10 ms 23900 KB Output is correct
74 Correct 10 ms 23972 KB Output is correct
75 Correct 9 ms 23744 KB Output is correct
76 Correct 13 ms 23900 KB Output is correct
77 Correct 10 ms 23900 KB Output is correct
78 Correct 11 ms 23808 KB Output is correct
79 Correct 9 ms 23900 KB Output is correct
80 Correct 9 ms 23768 KB Output is correct
81 Correct 9 ms 23844 KB Output is correct
82 Correct 10 ms 23900 KB Output is correct
83 Correct 10 ms 23900 KB Output is correct
84 Correct 10 ms 23900 KB Output is correct
85 Correct 10 ms 23896 KB Output is correct
86 Correct 9 ms 23912 KB Output is correct
87 Correct 10 ms 23900 KB Output is correct
88 Correct 9 ms 23900 KB Output is correct
89 Correct 12 ms 23900 KB Output is correct
90 Correct 13 ms 23900 KB Output is correct
91 Correct 11 ms 24032 KB Output is correct
92 Correct 9 ms 23896 KB Output is correct
93 Correct 9 ms 23900 KB Output is correct
94 Correct 11 ms 24028 KB Output is correct
95 Correct 11 ms 23900 KB Output is correct
96 Correct 11 ms 23944 KB Output is correct
97 Correct 10 ms 23896 KB Output is correct
98 Correct 9 ms 23900 KB Output is correct
99 Correct 10 ms 23900 KB Output is correct
# Verdict Execution time Memory Grader output
1 Correct 10 ms 23896 KB Output is correct
2 Correct 10 ms 23900 KB Output is correct
3 Correct 9 ms 23900 KB Output is correct
4 Correct 10 ms 23900 KB Output is correct
5 Correct 9 ms 23932 KB Output is correct
6 Correct 10 ms 23896 KB Output is correct
7 Correct 10 ms 23828 KB Output is correct
8 Correct 10 ms 23900 KB Output is correct
9 Correct 10 ms 23940 KB Output is correct
10 Correct 12 ms 23900 KB Output is correct
11 Correct 10 ms 23900 KB Output is correct
12 Correct 10 ms 23900 KB Output is correct
13 Correct 10 ms 23896 KB Output is correct
14 Correct 11 ms 23900 KB Output is correct
15 Correct 11 ms 23900 KB Output is correct
16 Correct 10 ms 23888 KB Output is correct
17 Correct 10 ms 23896 KB Output is correct
18 Correct 10 ms 23956 KB Output is correct
19 Correct 9 ms 23944 KB Output is correct
20 Correct 10 ms 23900 KB Output is correct
21 Correct 10 ms 23796 KB Output is correct
22 Correct 10 ms 23896 KB Output is correct
23 Correct 10 ms 23900 KB Output is correct
24 Correct 9 ms 23908 KB Output is correct
25 Correct 10 ms 23896 KB Output is correct
26 Correct 10 ms 23900 KB Output is correct
27 Correct 10 ms 23900 KB Output is correct
28 Correct 10 ms 23940 KB Output is correct
29 Correct 10 ms 23896 KB Output is correct
30 Correct 9 ms 23784 KB Output is correct
31 Correct 10 ms 23900 KB Output is correct
32 Correct 10 ms 23816 KB Output is correct
33 Correct 10 ms 23984 KB Output is correct
34 Correct 13 ms 23896 KB Output is correct
35 Correct 10 ms 23900 KB Output is correct
36 Correct 10 ms 23892 KB Output is correct
37 Correct 10 ms 23900 KB Output is correct
38 Correct 12 ms 23900 KB Output is correct
39 Correct 10 ms 23900 KB Output is correct
40 Correct 10 ms 23900 KB Output is correct
41 Correct 10 ms 23900 KB Output is correct
42 Correct 10 ms 24020 KB Output is correct
43 Correct 10 ms 23896 KB Output is correct
44 Correct 12 ms 23900 KB Output is correct
45 Correct 10 ms 23900 KB Output is correct
46 Correct 10 ms 23896 KB Output is correct
47 Correct 10 ms 23944 KB Output is correct
48 Correct 10 ms 23896 KB Output is correct
49 Correct 10 ms 23964 KB Output is correct
50 Correct 10 ms 23968 KB Output is correct
51 Correct 10 ms 23952 KB Output is correct
52 Correct 10 ms 23900 KB Output is correct
53 Correct 9 ms 23936 KB Output is correct
54 Correct 10 ms 23844 KB Output is correct
55 Correct 10 ms 23900 KB Output is correct
56 Correct 9 ms 23900 KB Output is correct
57 Correct 10 ms 23956 KB Output is correct
58 Correct 10 ms 23900 KB Output is correct
59 Correct 11 ms 23900 KB Output is correct
60 Correct 13 ms 23944 KB Output is correct
61 Correct 10 ms 23900 KB Output is correct
62 Correct 9 ms 23900 KB Output is correct
63 Correct 10 ms 23900 KB Output is correct
64 Correct 9 ms 23900 KB Output is correct
65 Correct 10 ms 23968 KB Output is correct
66 Correct 9 ms 23800 KB Output is correct
67 Correct 9 ms 23900 KB Output is correct
68 Correct 27 ms 31580 KB Output is correct
69 Correct 57 ms 39212 KB Output is correct
70 Correct 11 ms 24152 KB Output is correct
71 Correct 59 ms 46932 KB Output is correct
72 Correct 71 ms 54788 KB Output is correct
73 Correct 78 ms 62548 KB Output is correct
74 Correct 95 ms 70204 KB Output is correct
75 Correct 108 ms 77904 KB Output is correct
76 Correct 124 ms 85840 KB Output is correct
77 Correct 140 ms 93524 KB Output is correct
78 Correct 155 ms 101112 KB Output is correct
79 Correct 164 ms 108880 KB Output is correct
80 Correct 176 ms 116620 KB Output is correct
81 Correct 10 ms 23900 KB Output is correct
82 Correct 203 ms 124480 KB Output is correct
83 Correct 206 ms 132096 KB Output is correct
84 Correct 223 ms 139952 KB Output is correct
85 Correct 240 ms 147792 KB Output is correct
86 Correct 253 ms 155472 KB Output is correct
87 Correct 270 ms 163152 KB Output is correct
88 Correct 284 ms 170832 KB Output is correct
89 Correct 301 ms 178512 KB Output is correct
90 Correct 11 ms 23896 KB Output is correct
91 Correct 9 ms 23900 KB Output is correct
92 Correct 9 ms 23900 KB Output is correct
93 Correct 9 ms 23912 KB Output is correct
94 Correct 9 ms 23900 KB Output is correct
95 Correct 9 ms 23900 KB Output is correct
96 Correct 9 ms 23900 KB Output is correct
97 Correct 9 ms 23900 KB Output is correct
98 Correct 9 ms 23932 KB Output is correct
99 Correct 10 ms 23900 KB Output is correct
100 Correct 10 ms 23944 KB Output is correct
101 Correct 12 ms 23940 KB Output is correct
102 Correct 11 ms 23900 KB Output is correct
103 Correct 10 ms 23900 KB Output is correct
104 Correct 9 ms 23896 KB Output is correct
105 Correct 9 ms 23900 KB Output is correct
106 Correct 10 ms 23900 KB Output is correct
107 Correct 9 ms 23900 KB Output is correct
108 Correct 9 ms 23900 KB Output is correct
109 Correct 9 ms 23900 KB Output is correct
110 Correct 9 ms 23900 KB Output is correct
111 Correct 9 ms 23796 KB Output is correct
112 Correct 12 ms 23900 KB Output is correct
113 Correct 10 ms 23952 KB Output is correct
114 Correct 10 ms 23900 KB Output is correct
115 Correct 9 ms 23828 KB Output is correct
116 Correct 9 ms 23900 KB Output is correct
117 Correct 10 ms 23708 KB Output is correct
118 Correct 9 ms 23900 KB Output is correct
119 Correct 13 ms 23924 KB Output is correct
120 Correct 10 ms 23900 KB Output is correct
121 Correct 10 ms 23972 KB Output is correct
122 Correct 9 ms 23744 KB Output is correct
123 Correct 13 ms 23900 KB Output is correct
124 Correct 10 ms 23900 KB Output is correct
125 Correct 11 ms 23808 KB Output is correct
126 Correct 9 ms 23900 KB Output is correct
127 Correct 9 ms 23768 KB Output is correct
128 Correct 9 ms 23844 KB Output is correct
129 Correct 10 ms 23900 KB Output is correct
130 Correct 10 ms 23900 KB Output is correct
131 Correct 10 ms 23900 KB Output is correct
132 Correct 10 ms 23896 KB Output is correct
133 Correct 9 ms 23912 KB Output is correct
134 Correct 10 ms 23900 KB Output is correct
135 Correct 9 ms 23900 KB Output is correct
136 Correct 12 ms 23900 KB Output is correct
137 Correct 13 ms 23900 KB Output is correct
138 Correct 11 ms 24032 KB Output is correct
139 Correct 9 ms 23896 KB Output is correct
140 Correct 9 ms 23900 KB Output is correct
141 Correct 11 ms 24028 KB Output is correct
142 Correct 11 ms 23900 KB Output is correct
143 Correct 11 ms 23944 KB Output is correct
144 Correct 10 ms 23896 KB Output is correct
145 Correct 9 ms 23900 KB Output is correct
146 Correct 10 ms 23900 KB Output is correct
147 Correct 10 ms 23900 KB Output is correct
148 Correct 11 ms 23900 KB Output is correct
149 Correct 10 ms 23896 KB Output is correct
150 Correct 10 ms 23900 KB Output is correct
151 Correct 14 ms 23900 KB Output is correct
152 Correct 10 ms 23940 KB Output is correct
153 Correct 10 ms 23896 KB Output is correct
154 Correct 10 ms 23900 KB Output is correct
155 Correct 10 ms 23900 KB Output is correct
156 Correct 10 ms 23900 KB Output is correct
157 Correct 10 ms 23900 KB Output is correct
158 Correct 10 ms 23900 KB Output is correct
159 Correct 9 ms 23896 KB Output is correct
160 Correct 9 ms 23812 KB Output is correct
161 Correct 9 ms 23900 KB Output is correct
162 Correct 9 ms 23900 KB Output is correct
163 Correct 10 ms 23912 KB Output is correct
164 Correct 14 ms 23900 KB Output is correct
165 Correct 9 ms 23900 KB Output is correct
166 Correct 9 ms 23900 KB Output is correct
167 Correct 10 ms 23900 KB Output is correct
168 Correct 8 ms 23908 KB Output is correct
169 Correct 10 ms 23960 KB Output is correct
170 Correct 12 ms 23896 KB Output is correct
171 Correct 24 ms 27600 KB Output is correct
172 Correct 43 ms 31484 KB Output is correct
173 Correct 58 ms 35412 KB Output is correct
174 Correct 78 ms 39252 KB Output is correct
175 Correct 112 ms 43072 KB Output is correct
176 Correct 140 ms 46928 KB Output is correct
177 Correct 174 ms 50980 KB Output is correct
178 Correct 227 ms 54564 KB Output is correct
179 Correct 229 ms 58708 KB Output is correct
180 Correct 9 ms 23900 KB Output is correct
181 Correct 279 ms 62420 KB Output is correct
182 Correct 332 ms 66112 KB Output is correct
183 Correct 367 ms 70224 KB Output is correct
184 Correct 355 ms 74052 KB Output is correct
185 Correct 355 ms 77756 KB Output is correct
186 Correct 436 ms 81688 KB Output is correct
187 Correct 480 ms 85328 KB Output is correct
188 Correct 471 ms 89424 KB Output is correct
189 Correct 547 ms 93256 KB Output is correct
190 Correct 545 ms 97104 KB Output is correct
191 Correct 11 ms 23900 KB Output is correct
192 Correct 647 ms 100692 KB Output is correct
193 Correct 155 ms 99920 KB Output is correct
194 Correct 278 ms 176212 KB Output is correct
195 Correct 12 ms 23896 KB Output is correct
196 Correct 10 ms 23896 KB Output is correct
197 Correct 9 ms 23912 KB Output is correct
198 Correct 10 ms 23896 KB Output is correct