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답안 #1042839

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1042839 2024-08-03T12:56:10 Z Unforgettablepl Tricolor Lights (JOI24_tricolor) C++17
50 / 100
 260 ms 46808 KB 
#include "Anna.h"
#include <bits/stdc++.h>
using namespace std;

namespace {

string calc(vector<int> arr,string S){
	int N = S.size();
	string res(N,'$');
	for(int i=0;i<N-1;i++){
		if(arr[i])continue;
		{
			vector<bool> present(3);
			if(S[i]=='R')present[0]=true;
			else if(S[i]=='G')present[1]=true;
			else if(S[i]=='B')present[2]=true;
			if(S[i+1]=='R')present[0]=true;
			else if(S[i+1]=='G')present[1]=true;
			else if(S[i+1]=='B')present[2]=true;
			if(!present[0])res[i]=res[i+1]='R';
			else if(!present[1])res[i]=res[i+1]='G';
			else if(!present[2])res[i]=res[i+1]='B';
		}
		for(int j=i-1;j>=0;j--){
			if(arr[j]!=1)break;
			vector<bool> present(3);
			if(S[j]=='R')present[0]=true;
			else if(S[j]=='G')present[1]=true;
			else if(S[j]=='B')present[2]=true;
			if(res[j+1]=='R')present[0]=true;
			else if(res[j+1]=='G')present[1]=true;
			else if(res[j+1]=='B')present[2]=true;
			if(!present[0])res[j]='R';
			else if(!present[1])res[j]='G';
			else if(!present[2])res[j]='B';
		}
		for(int j=i+2;j<N;j++){
			if(arr[j-1]!=1)break;
			vector<bool> present(3);
			if(S[j]=='R')present[0]=true;
			else if(S[j]=='G')present[1]=true;
			else if(S[j]=='B')present[2]=true;
			if(res[j-1]=='R')present[0]=true;
			else if(res[j-1]=='G')present[1]=true;
			else if(res[j-1]=='B')present[2]=true;
			if(!present[0])res[j]='R';
			else if(!present[1])res[j]='G';
			else if(!present[2])res[j]='B';	
		}
	}
	for(int i=0;i<N;i++){
		if(res[i]=='$'){
			if(S[i]=='R')res[i]='B';
			else if(S[i]=='B')res[i]='G';
			else if(S[i]=='G')res[i]='R';
		}
		for(int j=i+1;j<N;j++){
			if(arr[j-1]!=1)break;
			vector<bool> present(3);
			if(S[j]=='R')present[0]=true;
			else if(S[j]=='G')present[1]=true;
			else if(S[j]=='B')present[2]=true;
			if(res[j-1]=='R')present[0]=true;
			else if(res[j-1]=='G')present[1]=true;
			else if(res[j-1]=='B')present[2]=true;
			if(!present[0])res[j]='R';
			else if(!present[1])res[j]='G';
			else if(!present[2])res[j]='B';	
		}
	}
	return res;
}


vector<int> generateDe(int n){
	vector<int> debrujin;
	n--;
	vector<pair<bool,bool>> visited(1<<n);
	function<void(int)> dfs = [&](int x){
		if(!visited[x].first){
			visited[x].first=true;
			dfs((x<<1)&((1<<n)-1));
			debrujin.emplace_back(0);
		}
		if(!visited[x].second){
			visited[x].second=true;
			dfs(((x<<1)&((1<<n)-1))+1);
			debrujin.emplace_back(1);
		}
	};
	dfs(0);
	for(int i=1;i<=n;i++)debrujin.emplace_back(0);
	return debrujin;
}

}

pair<string, int> anna(int N, string S) {
	if(N<=59){
		string res;
		for(int i=0;i<N;i++){
			if(S[i]=='R')res.insert(res.end(),'B');
			else if(S[i]=='B')res.insert(res.end(),'G');
			else if(S[i]=='G')res.insert(res.end(),'R');
		}
		return {res,N};
	}
	auto debrujin = generateDe(18);
	vector<int> res(N+6,2);
	int itr = 0;
	for(int i=0;i<N;i+=3){
		if(debrujin[itr++]==0){
			res[i]=0;
			res[i+1]=1;
		} else {
			res[i-1]=res[i]=res[i+1]=1;
		}
	}
	return {calc(res,S),59};
}
#include "Bruno.h"
#include <bits/stdc++.h>
using namespace std;

namespace {

int N;
int l;

vector<int> generateDe(int n){
	vector<int> debrujin;
	n--;
	vector<pair<bool,bool>> visited(1<<n);
	function<void(int)> dfs = [&](int x){
		if(!visited[x].first){
			visited[x].first=true;
			dfs((x<<1)&((1<<n)-1));
			debrujin.emplace_back(0);
		}
		if(!visited[x].second){
			visited[x].second=true;
			dfs(((x<<1)&((1<<n)-1))+1);
			debrujin.emplace_back(1);
		}
	};
	dfs(0);
	for(int i=1;i<=n;i++)debrujin.emplace_back(0);
	return debrujin;
}

vector<int> debrujin;
map<int,int> lookup;

}  // namespace

void init(int N, int l) {
	::N = N;
	::l = l;
	debrujin = generateDe(18);
	for(int i=0;i<N;i++){
		int curr = 0;
		for(int j=0;j<18;j++){
			if(debrujin[i+j])curr|=(1<<j);
		}
		lookup[curr]=i;
	}
}

int bruno(string u) {
	if(N<=59)return 1;
	vector<int> res(l-1);
	for(int i=0;i<l-1;i++)res[i]=u[i]!=u[i+1];
	bool found = false;
	int offset = 0;
	for(int i=0;i<l-2;i++){
		if(res[i])continue;
		if(res[i+1]==0)offset=(i+1)%3;
		else offset = i%3;
		found = true;
		break;
	}
	assert(found);
	vector<int> myseq;
	for(int i=offset;i<l-1;i+=3){
		if(myseq.size()==18)break;
		myseq.emplace_back(res[i]);
	}
	int curr = 0;
	for(int i=0;i<18;i++){
		if(myseq[i])curr|=(1<<i);
	}
	return lookup[curr]*3+1-offset;
	assert(false);
}

Subtask #1
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 42 ms 15912 KB Output is correct
2 Correct 36 ms 16056 KB Output is correct
3 Correct 37 ms 15968 KB Output is correct
4 Correct 38 ms 15992 KB Output is correct
5 Correct 53 ms 30748 KB Output is correct
6 Correct 53 ms 30744 KB Output is correct
7 Correct 60 ms 30568 KB Output is correct
8 Correct 55 ms 30620 KB Output is correct
9 Correct 37 ms 15944 KB Output is correct
10 Correct 37 ms 15984 KB Output is correct
11 Correct 36 ms 16104 KB Output is correct
12 Correct 38 ms 16132 KB Output is correct
13 Correct 41 ms 15964 KB Output is correct
14 Correct 38 ms 15996 KB Output is correct
15 Correct 52 ms 15916 KB Output is correct
16 Correct 56 ms 16048 KB Output is correct
17 Correct 41 ms 15948 KB Output is correct
18 Correct 38 ms 15968 KB Output is correct
19 Correct 39 ms 15920 KB Output is correct
20 Correct 39 ms 15968 KB Output is correct
21 Correct 39 ms 15904 KB Output is correct
22 Correct 62 ms 16004 KB Output is correct
23 Correct 41 ms 15928 KB Output is correct
24 Correct 40 ms 15928 KB Output is correct
25 Correct 38 ms 15948 KB Output is correct
26 Correct 76 ms 30624 KB Output is correct
27 Correct 56 ms 30808 KB Output is correct
28 Correct 57 ms 30748 KB Output is correct
29 Correct 54 ms 30788 KB Output is correct
30 Correct 56 ms 30620 KB Output is correct
31 Correct 57 ms 30844 KB Output is correct
32 Correct 66 ms 30700 KB Output is correct
33 Correct 55 ms 30624 KB Output is correct
34 Correct 54 ms 15932 KB Output is correct
35 Correct 41 ms 15920 KB Output is correct
36 Correct 57 ms 30596 KB Output is correct
37 Correct 61 ms 30800 KB Output is correct
38 Correct 60 ms 30624 KB Output is correct
39 Correct 59 ms 30624 KB Output is correct
40 Correct 59 ms 30768 KB Output is correct
41 Correct 57 ms 30644 KB Output is correct
42 Correct 56 ms 30704 KB Output is correct

Subtask #2
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 42 ms 15912 KB Output is correct
2 Correct 36 ms 16056 KB Output is correct
3 Correct 37 ms 15968 KB Output is correct
4 Correct 38 ms 15992 KB Output is correct
5 Correct 53 ms 30748 KB Output is correct
6 Correct 53 ms 30744 KB Output is correct
7 Correct 60 ms 30568 KB Output is correct
8 Correct 55 ms 30620 KB Output is correct
9 Correct 37 ms 15944 KB Output is correct
10 Correct 37 ms 15984 KB Output is correct
11 Correct 36 ms 16104 KB Output is correct
12 Correct 38 ms 16132 KB Output is correct
13 Correct 41 ms 15964 KB Output is correct
14 Correct 38 ms 15996 KB Output is correct
15 Correct 52 ms 15916 KB Output is correct
16 Correct 56 ms 16048 KB Output is correct
17 Correct 41 ms 15948 KB Output is correct
18 Correct 38 ms 15968 KB Output is correct
19 Correct 39 ms 15920 KB Output is correct
20 Correct 39 ms 15968 KB Output is correct
21 Correct 39 ms 15904 KB Output is correct
22 Correct 62 ms 16004 KB Output is correct
23 Correct 41 ms 15928 KB Output is correct
24 Correct 40 ms 15928 KB Output is correct
25 Correct 38 ms 15948 KB Output is correct
26 Correct 76 ms 30624 KB Output is correct
27 Correct 56 ms 30808 KB Output is correct
28 Correct 57 ms 30748 KB Output is correct
29 Correct 54 ms 30788 KB Output is correct
30 Correct 56 ms 30620 KB Output is correct
31 Correct 57 ms 30844 KB Output is correct
32 Correct 66 ms 30700 KB Output is correct
33 Correct 55 ms 30624 KB Output is correct
34 Correct 54 ms 15932 KB Output is correct
35 Correct 41 ms 15920 KB Output is correct
36 Correct 57 ms 30596 KB Output is correct
37 Correct 61 ms 30800 KB Output is correct
38 Correct 60 ms 30624 KB Output is correct
39 Correct 59 ms 30624 KB Output is correct
40 Correct 59 ms 30768 KB Output is correct
41 Correct 57 ms 30644 KB Output is correct
42 Correct 56 ms 30704 KB Output is correct
43 Correct 60 ms 30568 KB Output is correct
44 Correct 60 ms 30740 KB Output is correct
45 Correct 60 ms 30620 KB Output is correct
46 Correct 59 ms 30528 KB Output is correct
47 Correct 65 ms 30640 KB Output is correct
48 Correct 60 ms 30728 KB Output is correct
49 Correct 65 ms 30592 KB Output is correct
50 Correct 55 ms 31752 KB Output is correct
51 Correct 57 ms 30728 KB Output is correct
52 Correct 77 ms 30624 KB Output is correct
53 Correct 55 ms 30604 KB Output is correct

Subtask #3
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 42 ms 15912 KB Output is correct
2 Correct 36 ms 16056 KB Output is correct
3 Correct 37 ms 15968 KB Output is correct
4 Correct 38 ms 15992 KB Output is correct
5 Correct 53 ms 30748 KB Output is correct
6 Correct 53 ms 30744 KB Output is correct
7 Correct 60 ms 30568 KB Output is correct
8 Correct 55 ms 30620 KB Output is correct
9 Correct 37 ms 15944 KB Output is correct
10 Correct 37 ms 15984 KB Output is correct
11 Correct 36 ms 16104 KB Output is correct
12 Correct 38 ms 16132 KB Output is correct
13 Correct 41 ms 15964 KB Output is correct
14 Correct 38 ms 15996 KB Output is correct
15 Correct 52 ms 15916 KB Output is correct
16 Correct 56 ms 16048 KB Output is correct
17 Correct 41 ms 15948 KB Output is correct
18 Correct 38 ms 15968 KB Output is correct
19 Correct 39 ms 15920 KB Output is correct
20 Correct 39 ms 15968 KB Output is correct
21 Correct 39 ms 15904 KB Output is correct
22 Correct 62 ms 16004 KB Output is correct
23 Correct 41 ms 15928 KB Output is correct
24 Correct 40 ms 15928 KB Output is correct
25 Correct 38 ms 15948 KB Output is correct
26 Correct 76 ms 30624 KB Output is correct
27 Correct 56 ms 30808 KB Output is correct
28 Correct 57 ms 30748 KB Output is correct
29 Correct 54 ms 30788 KB Output is correct
30 Correct 56 ms 30620 KB Output is correct
31 Correct 57 ms 30844 KB Output is correct
32 Correct 66 ms 30700 KB Output is correct
33 Correct 55 ms 30624 KB Output is correct
34 Correct 54 ms 15932 KB Output is correct
35 Correct 41 ms 15920 KB Output is correct
36 Correct 57 ms 30596 KB Output is correct
37 Correct 61 ms 30800 KB Output is correct
38 Correct 60 ms 30624 KB Output is correct
39 Correct 59 ms 30624 KB Output is correct
40 Correct 59 ms 30768 KB Output is correct
41 Correct 57 ms 30644 KB Output is correct
42 Correct 56 ms 30704 KB Output is correct
43 Correct 60 ms 30568 KB Output is correct
44 Correct 60 ms 30740 KB Output is correct
45 Correct 60 ms 30620 KB Output is correct
46 Correct 59 ms 30528 KB Output is correct
47 Correct 65 ms 30640 KB Output is correct
48 Correct 60 ms 30728 KB Output is correct
49 Correct 65 ms 30592 KB Output is correct
50 Correct 55 ms 31752 KB Output is correct
51 Correct 57 ms 30728 KB Output is correct
52 Correct 77 ms 30624 KB Output is correct
53 Correct 55 ms 30604 KB Output is correct
54 Correct 69 ms 30652 KB Output is correct
55 Correct 60 ms 30732 KB Output is correct
56 Correct 54 ms 30856 KB Output is correct
57 Correct 54 ms 30744 KB Output is correct
58 Correct 56 ms 30752 KB Output is correct
59 Correct 56 ms 30628 KB Output is correct
60 Correct 58 ms 30568 KB Output is correct
61 Correct 54 ms 30664 KB Output is correct
62 Correct 58 ms 30884 KB Output is correct
63 Correct 56 ms 30828 KB Output is correct
64 Correct 57 ms 30700 KB Output is correct
65 Correct 55 ms 30620 KB Output is correct
66 Correct 57 ms 30656 KB Output is correct
67 Correct 62 ms 30620 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 42 ms 15912 KB Output is correct
2 Correct 36 ms 16056 KB Output is correct
3 Correct 37 ms 15968 KB Output is correct
4 Correct 38 ms 15992 KB Output is correct
5 Correct 53 ms 30748 KB Output is correct
6 Correct 53 ms 30744 KB Output is correct
7 Correct 60 ms 30568 KB Output is correct
8 Correct 55 ms 30620 KB Output is correct
9 Correct 37 ms 15944 KB Output is correct
10 Correct 37 ms 15984 KB Output is correct
11 Correct 36 ms 16104 KB Output is correct
12 Correct 38 ms 16132 KB Output is correct
13 Correct 41 ms 15964 KB Output is correct
14 Correct 38 ms 15996 KB Output is correct
15 Correct 52 ms 15916 KB Output is correct
16 Correct 56 ms 16048 KB Output is correct
17 Correct 41 ms 15948 KB Output is correct
18 Correct 38 ms 15968 KB Output is correct
19 Correct 39 ms 15920 KB Output is correct
20 Correct 39 ms 15968 KB Output is correct
21 Correct 39 ms 15904 KB Output is correct
22 Correct 62 ms 16004 KB Output is correct
23 Correct 41 ms 15928 KB Output is correct
24 Correct 40 ms 15928 KB Output is correct
25 Correct 38 ms 15948 KB Output is correct
26 Correct 76 ms 30624 KB Output is correct
27 Correct 56 ms 30808 KB Output is correct
28 Correct 57 ms 30748 KB Output is correct
29 Correct 54 ms 30788 KB Output is correct
30 Correct 56 ms 30620 KB Output is correct
31 Correct 57 ms 30844 KB Output is correct
32 Correct 66 ms 30700 KB Output is correct
33 Correct 55 ms 30624 KB Output is correct
34 Correct 54 ms 15932 KB Output is correct
35 Correct 41 ms 15920 KB Output is correct
36 Correct 57 ms 30596 KB Output is correct
37 Correct 61 ms 30800 KB Output is correct
38 Correct 60 ms 30624 KB Output is correct
39 Correct 59 ms 30624 KB Output is correct
40 Correct 59 ms 30768 KB Output is correct
41 Correct 57 ms 30644 KB Output is correct
42 Correct 56 ms 30704 KB Output is correct
43 Correct 60 ms 30568 KB Output is correct
44 Correct 60 ms 30740 KB Output is correct
45 Correct 60 ms 30620 KB Output is correct
46 Correct 59 ms 30528 KB Output is correct
47 Correct 65 ms 30640 KB Output is correct
48 Correct 60 ms 30728 KB Output is correct
49 Correct 65 ms 30592 KB Output is correct
50 Correct 55 ms 31752 KB Output is correct
51 Correct 57 ms 30728 KB Output is correct
52 Correct 77 ms 30624 KB Output is correct
53 Correct 55 ms 30604 KB Output is correct
54 Correct 69 ms 30652 KB Output is correct
55 Correct 60 ms 30732 KB Output is correct
56 Correct 54 ms 30856 KB Output is correct
57 Correct 54 ms 30744 KB Output is correct
58 Correct 56 ms 30752 KB Output is correct
59 Correct 56 ms 30628 KB Output is correct
60 Correct 58 ms 30568 KB Output is correct
61 Correct 54 ms 30664 KB Output is correct
62 Correct 58 ms 30884 KB Output is correct
63 Correct 56 ms 30828 KB Output is correct
64 Correct 57 ms 30700 KB Output is correct
65 Correct 55 ms 30620 KB Output is correct
66 Correct 57 ms 30656 KB Output is correct
67 Correct 62 ms 30620 KB Output is correct
68 Correct 59 ms 30644 KB Output is correct
69 Correct 60 ms 30752 KB Output is correct
70 Correct 62 ms 30624 KB Output is correct
71 Correct 62 ms 30540 KB Output is correct
72 Correct 61 ms 30564 KB Output is correct
73 Correct 56 ms 30740 KB Output is correct
74 Correct 63 ms 30624 KB Output is correct
75 Correct 65 ms 30660 KB Output is correct
76 Correct 57 ms 30728 KB Output is correct
77 Correct 59 ms 30568 KB Output is correct
78 Correct 96 ms 30596 KB Output is correct
79 Correct 88 ms 30628 KB Output is correct

Subtask #5
19.99998 / 70.0

# 결과 실행 시간 메모리 Grader output
1 Correct 37 ms 15956 KB Output is correct
2 Correct 36 ms 15928 KB Output is correct
3 Correct 35 ms 16012 KB Output is correct
4 Correct 37 ms 15996 KB Output is correct
5 Partially correct 86 ms 30736 KB Partially correct
6 Partially correct 57 ms 30664 KB Partially correct
7 Partially correct 53 ms 30740 KB Partially correct
8 Partially correct 80 ms 30624 KB Partially correct
9 Partially correct 63 ms 30624 KB Partially correct
10 Partially correct 59 ms 30600 KB Partially correct
11 Partially correct 61 ms 30704 KB Partially correct
12 Partially correct 53 ms 30756 KB Partially correct
13 Partially correct 68 ms 30624 KB Partially correct
14 Partially correct 62 ms 30704 KB Partially correct
15 Partially correct 224 ms 46772 KB Partially correct
16 Partially correct 209 ms 46712 KB Partially correct
17 Partially correct 204 ms 46456 KB Partially correct
18 Correct 41 ms 15856 KB Output is correct
19 Correct 55 ms 15932 KB Output is correct
20 Correct 40 ms 15932 KB Output is correct
21 Correct 40 ms 15920 KB Output is correct
22 Correct 38 ms 15996 KB Output is correct
23 Partially correct 39 ms 15916 KB Partially correct
24 Partially correct 41 ms 15928 KB Partially correct
25 Partially correct 41 ms 16112 KB Partially correct
26 Partially correct 40 ms 15916 KB Partially correct
27 Partially correct 45 ms 15996 KB Partially correct
28 Partially correct 44 ms 15996 KB Partially correct
29 Partially correct 45 ms 15956 KB Partially correct
30 Partially correct 56 ms 15964 KB Partially correct
31 Partially correct 48 ms 15936 KB Partially correct
32 Partially correct 40 ms 15948 KB Partially correct
33 Partially correct 54 ms 15928 KB Partially correct
34 Partially correct 45 ms 15916 KB Partially correct
35 Partially correct 61 ms 30652 KB Partially correct
36 Partially correct 57 ms 30604 KB Partially correct
37 Partially correct 60 ms 30676 KB Partially correct
38 Partially correct 68 ms 30620 KB Partially correct
39 Partially correct 62 ms 30676 KB Partially correct
40 Partially correct 63 ms 30732 KB Partially correct
41 Partially correct 57 ms 30776 KB Partially correct
42 Partially correct 71 ms 30608 KB Partially correct
43 Partially correct 66 ms 30780 KB Partially correct
44 Partially correct 60 ms 30728 KB Partially correct
45 Partially correct 70 ms 30724 KB Partially correct
46 Partially correct 57 ms 30768 KB Partially correct
47 Partially correct 62 ms 30732 KB Partially correct
48 Partially correct 56 ms 30736 KB Partially correct
49 Partially correct 69 ms 30624 KB Partially correct
50 Partially correct 61 ms 30936 KB Partially correct
51 Partially correct 57 ms 30672 KB Partially correct
52 Partially correct 57 ms 30732 KB Partially correct
53 Partially correct 61 ms 30668 KB Partially correct
54 Partially correct 104 ms 34424 KB Partially correct
55 Partially correct 246 ms 46592 KB Partially correct
56 Partially correct 260 ms 46552 KB Partially correct
57 Partially correct 230 ms 46496 KB Partially correct
58 Correct 42 ms 16000 KB Output is correct
59 Correct 44 ms 15948 KB Output is correct
60 Partially correct 64 ms 30692 KB Partially correct
61 Partially correct 63 ms 30716 KB Partially correct
62 Partially correct 61 ms 30752 KB Partially correct
63 Partially correct 54 ms 30624 KB Partially correct
64 Partially correct 60 ms 30740 KB Partially correct
65 Partially correct 61 ms 30768 KB Partially correct
66 Partially correct 65 ms 30656 KB Partially correct
67 Partially correct 63 ms 30672 KB Partially correct
68 Partially correct 59 ms 30640 KB Partially correct
69 Partially correct 232 ms 46480 KB Partially correct
70 Partially correct 244 ms 46808 KB Partially correct
71 Partially correct 217 ms 46456 KB Partially correct
72 Partially correct 57 ms 30620 KB Partially correct
73 Partially correct 75 ms 30588 KB Partially correct
74 Partially correct 53 ms 30696 KB Partially correct
75 Partially correct 58 ms 30620 KB Partially correct
76 Partially correct 60 ms 30664 KB Partially correct
77 Partially correct 57 ms 30708 KB Partially correct
78 Partially correct 207 ms 46456 KB Partially correct
79 Partially correct 228 ms 46456 KB Partially correct
80 Partially correct 223 ms 46736 KB Partially correct
81 Partially correct 75 ms 30948 KB Partially correct
82 Partially correct 60 ms 30620 KB Partially correct
83 Partially correct 64 ms 30532 KB Partially correct
84 Partially correct 71 ms 30620 KB Partially correct
85 Partially correct 64 ms 30696 KB Partially correct
86 Partially correct 57 ms 30660 KB Partially correct
87 Partially correct 69 ms 30624 KB Partially correct
88 Partially correct 55 ms 30632 KB Partially correct
89 Partially correct 57 ms 30752 KB Partially correct
90 Partially correct 70 ms 30676 KB Partially correct
91 Partially correct 65 ms 30628 KB Partially correct
92 Partially correct 61 ms 30712 KB Partially correct
93 Partially correct 226 ms 46712 KB Partially correct
94 Partially correct 224 ms 46668 KB Partially correct
95 Partially correct 219 ms 46496 KB Partially correct