답안 #633832

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
633832 2022-08-23T09:35:02 Z IWTIM Copy and Paste 3 (JOI22_copypaste3) C++14
100 / 100
490 ms 69576 KB
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python! 
 
// pairs
using pii = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
#define mp make_pair
#define f first
#define s second
 
#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pii>;
using vpl = V<pl>;
using vpd = V<pd>;
 
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend() 
#define sor(x) sort(all(x)) 
#define rsz resize
#define ins insert 
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
 
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define rep(a) F0R(_,a)
#define each(a,x) for (auto& a: x)
const int MOD = 998244353;
const int MX = 2e5+5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1,0,-1,0}, dy[4]{0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;
struct DSU {
	vi e; void init(int N) { e = vi(N,-1); }
	int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); } 
	bool sameSet(int a, int b) { return get(a) == get(b); }
	int size(int x) { return -e[get(x)]; }
	bool unite(int x, int y) { // union by size
		x = get(x), y = get(y); if (x == y) return 0;
		if (e[x] > e[y]) swap(x,y);
		e[x] += e[y]; e[y] = x; return 1;
	}
};
/*
inline namespace Helpers {
	//////////// is_iterable
	// https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
	// this gets used only when we can call begin() and end() on that type
	tcT, class = void> struct is_iterable : false_type {};
	tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
	                                  decltype(end(declval<T>()))
	                                 >
	                       > : true_type {};
	tcT> constexpr bool is_iterable_v = is_iterable<T>::value;
 
	//////////// is_readable
	tcT, class = void> struct is_readable : false_type {};
	tcT> struct is_readable<T,
	        typename std::enable_if_t<
	            is_same_v<decltype(cin >> declval<T&>()), istream&>
	        >
	    > : true_type {};
	tcT> constexpr bool is_readable_v = is_readable<T>::value;
 
	//////////// is_printable
	// // https://nafe.es/posts/2020-02-29-is-printable/
	tcT, class = void> struct is_printable : false_type {};
	tcT> struct is_printable<T,
	        typename std::enable_if_t<
	            is_same_v<decltype(cout << declval<T>()), ostream&>
	        >
	    > : true_type {};
	tcT> constexpr bool is_printable_v = is_printable<T>::value;
}*/
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python! 
 
// pairs
using pii = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
#define mp make_pair
#define f first
#define s second
 
#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pii>;
using vpl = V<pl>;
using vpd = V<pd>;
 
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend() 
#define sor(x) sort(all(x)) 
#define rsz resize
#define ins insert 
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
 
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define rep(a) F0R(_,a)
#define each(a,x) for (auto& a: x)
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;
 
/*
inline namespace Helpers {
	//////////// is_iterable
	// https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
	// this gets used only when we can call begin() and end() on that type
	tcT, class = void> struct is_iterable : false_type {};
	tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
	                                  decltype(end(declval<T>()))
	                                 >
	                       > : true_type {};
	tcT> constexpr bool is_iterable_v = is_iterable<T>::value;
 
	//////////// is_readable
	tcT, class = void> struct is_readable : false_type {};
	tcT> struct is_readable<T,
	        typename std::enable_if_t<
	            is_same_v<decltype(cin >> declval<T&>()), istream&>
	        >
	    > : true_type {};
	tcT> constexpr bool is_readable_v = is_readable<T>::value;
 
	//////////// is_printable
	// // https://nafe.es/posts/2020-02-29-is-printable/
	tcT, class = void> struct is_printable : false_type {};
	tcT> struct is_printable<T,
	        typename std::enable_if_t<
	            is_same_v<decltype(cout << declval<T>()), ostream&>
	        >
	    > : true_type {};
	tcT> constexpr bool is_printable_v = is_printable<T>::value;
}*/
#define pb push_back
#define f first
#define s second
#define int long long
#define pii pair <int, int>
const int N = 3005, mod = 1e9 + 7;
int t,n,a,b,c,nxt[N], dp[N][N],pw[N],p;
vector < pii > v;
int hs[N][N];
string s;
int get(char ch) {
	return (ch - 'a' + 1);
}
void go(vector <int> vv, int sz) {
	int cur = -1;
	for (int i = (int)vv.size() - 1; i >= 0; i--) {
		while(true) {
			if (vv.back() >= vv[i] + sz) {
				cur = vv.back();
				vv.pop_back();
			} else break;
		}
		nxt[vv[i]] = cur;
	}
}
main() {
	p = 37;
    cin>>n>>s>>a>>b>>c;
    s = "@" + s;
    for (int i = 1; i <= n; i++) {
    	for (int j = i; j <= n; j++) {
    		dp[i][j] = (j - i + 1)*a;
		}
	}
	pw[0] = 1;
	for (int i = 1; i <= n; i++) {
		pw[i] = (pw[i - 1] * p) % mod;
	}
	for (int i = 1; i <= n; i++) {
		int curhs = 0;
		for (int j = i; j <= n; j++) {
			curhs = (curhs * p + get(s[j])) % mod;  
			hs[i][j] = curhs;
		}
	}
	for (int sz = 1; sz <= n; sz++) {
		v.clear();
		for (int j = 1; j + sz - 1 <= n; j++) {
			v.pb({hs[j][j + sz - 1], j});
		}
		
		sort(v.begin(),v.end());
		v.pb({-1, 0});
		int le = 0;
		for (int i = 1; i < v.size(); i++) {
			if (v[i].f != v[i - 1].f) {
				int ri = i - 1;
				vector <int> vv;
				for (int j = le; j <= ri; j++) {
					vv.pb(v[j].s);
				}
				go(vv,sz);
				le = i;
			}
		}
		
		for (int l = 1; l + sz - 1 <= n; l++) {
			if (sz > 1) dp[l][l + sz - 1] = min(dp[l][l + sz - 1], min(dp[l + 1][l + sz - 1] + a, dp[l][l + sz - 2] + a)); 
		}
		for (int l = 1; l + sz - 1 <= n; l++) {
			int curl = l;
			int cnt = 1;
			while (nxt[curl] != -1) {
				cnt++;
				int ri = nxt[curl] + sz - 1;
				dp[l][nxt[curl] + sz - 1] = min(dp[l][nxt[curl] + sz - 1], dp[l][l + sz - 1] + b + cnt * c + (ri - l + 1 - sz * cnt)*a);
			    curl = nxt[curl];
			}
		}
	}
	cout<<dp[1][n]<<"\n";
}

Compilation message

copypaste3.cpp:206:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  206 | main() {
      | ^~~~
copypaste3.cpp: In function 'int main()':
copypaste3.cpp:235:21: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<std::pair<long long int, long long int>, std::allocator<std::pair<long long int, long long int> > >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  235 |   for (int i = 1; i < v.size(); i++) {
      |                   ~~^~~~~~~~~~
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 468 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 211 ms 41292 KB Output is correct
4 Correct 229 ms 46836 KB Output is correct
5 Correct 240 ms 53432 KB Output is correct
6 Correct 319 ms 60848 KB Output is correct
7 Correct 350 ms 69476 KB Output is correct
8 Correct 357 ms 69472 KB Output is correct
9 Correct 337 ms 69476 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 0 ms 340 KB Output is correct
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 468 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 0 ms 340 KB Output is correct
18 Correct 0 ms 212 KB Output is correct
19 Correct 0 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 468 KB Output is correct
22 Correct 0 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 1 ms 468 KB Output is correct
25 Correct 1 ms 468 KB Output is correct
26 Correct 1 ms 468 KB Output is correct
27 Correct 1 ms 468 KB Output is correct
28 Correct 1 ms 468 KB Output is correct
29 Correct 1 ms 468 KB Output is correct
30 Correct 1 ms 468 KB Output is correct
31 Correct 1 ms 468 KB Output is correct
32 Correct 1 ms 468 KB Output is correct
33 Correct 0 ms 468 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 0 ms 340 KB Output is correct
36 Correct 0 ms 340 KB Output is correct
37 Correct 1 ms 340 KB Output is correct
38 Correct 1 ms 340 KB Output is correct
39 Correct 0 ms 468 KB Output is correct
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 468 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 0 ms 340 KB Output is correct
18 Correct 0 ms 212 KB Output is correct
19 Correct 0 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 468 KB Output is correct
22 Correct 0 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 1 ms 468 KB Output is correct
25 Correct 1 ms 468 KB Output is correct
26 Correct 1 ms 468 KB Output is correct
27 Correct 1 ms 468 KB Output is correct
28 Correct 1 ms 468 KB Output is correct
29 Correct 1 ms 468 KB Output is correct
30 Correct 1 ms 468 KB Output is correct
31 Correct 1 ms 468 KB Output is correct
32 Correct 1 ms 468 KB Output is correct
33 Correct 0 ms 468 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 0 ms 340 KB Output is correct
36 Correct 0 ms 340 KB Output is correct
37 Correct 1 ms 340 KB Output is correct
38 Correct 1 ms 340 KB Output is correct
39 Correct 0 ms 468 KB Output is correct
40 Correct 1 ms 980 KB Output is correct
41 Correct 2 ms 2260 KB Output is correct
42 Correct 3 ms 2260 KB Output is correct
43 Correct 3 ms 2260 KB Output is correct
44 Correct 3 ms 2260 KB Output is correct
45 Correct 3 ms 2260 KB Output is correct
46 Correct 3 ms 2260 KB Output is correct
47 Correct 4 ms 2152 KB Output is correct
48 Correct 13 ms 2224 KB Output is correct
49 Correct 8 ms 2260 KB Output is correct
50 Correct 5 ms 2260 KB Output is correct
51 Correct 4 ms 2260 KB Output is correct
52 Correct 4 ms 2260 KB Output is correct
53 Correct 4 ms 2260 KB Output is correct
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 0 ms 340 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 ms 468 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 0 ms 340 KB Output is correct
18 Correct 0 ms 212 KB Output is correct
19 Correct 0 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 468 KB Output is correct
22 Correct 0 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 1 ms 468 KB Output is correct
25 Correct 1 ms 468 KB Output is correct
26 Correct 1 ms 468 KB Output is correct
27 Correct 1 ms 468 KB Output is correct
28 Correct 1 ms 468 KB Output is correct
29 Correct 1 ms 468 KB Output is correct
30 Correct 1 ms 468 KB Output is correct
31 Correct 1 ms 468 KB Output is correct
32 Correct 1 ms 468 KB Output is correct
33 Correct 0 ms 468 KB Output is correct
34 Correct 0 ms 212 KB Output is correct
35 Correct 0 ms 340 KB Output is correct
36 Correct 0 ms 340 KB Output is correct
37 Correct 1 ms 340 KB Output is correct
38 Correct 1 ms 340 KB Output is correct
39 Correct 0 ms 468 KB Output is correct
40 Correct 1 ms 980 KB Output is correct
41 Correct 2 ms 2260 KB Output is correct
42 Correct 3 ms 2260 KB Output is correct
43 Correct 3 ms 2260 KB Output is correct
44 Correct 3 ms 2260 KB Output is correct
45 Correct 3 ms 2260 KB Output is correct
46 Correct 3 ms 2260 KB Output is correct
47 Correct 4 ms 2152 KB Output is correct
48 Correct 13 ms 2224 KB Output is correct
49 Correct 8 ms 2260 KB Output is correct
50 Correct 5 ms 2260 KB Output is correct
51 Correct 4 ms 2260 KB Output is correct
52 Correct 4 ms 2260 KB Output is correct
53 Correct 4 ms 2260 KB Output is correct
54 Correct 12 ms 5460 KB Output is correct
55 Correct 38 ms 16332 KB Output is correct
56 Correct 60 ms 16244 KB Output is correct
57 Correct 65 ms 16256 KB Output is correct
58 Correct 67 ms 16224 KB Output is correct
59 Correct 70 ms 16244 KB Output is correct
60 Correct 61 ms 16248 KB Output is correct
61 Correct 68 ms 16212 KB Output is correct
62 Correct 46 ms 16252 KB Output is correct
63 Correct 65 ms 16248 KB Output is correct
64 Correct 67 ms 16248 KB Output is correct
65 Correct 70 ms 16248 KB Output is correct
66 Correct 66 ms 16252 KB Output is correct
67 Correct 59 ms 16248 KB Output is correct
# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 340 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 211 ms 41292 KB Output is correct
14 Correct 229 ms 46836 KB Output is correct
15 Correct 240 ms 53432 KB Output is correct
16 Correct 319 ms 60848 KB Output is correct
17 Correct 350 ms 69476 KB Output is correct
18 Correct 357 ms 69472 KB Output is correct
19 Correct 337 ms 69476 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 468 KB Output is correct
27 Correct 0 ms 340 KB Output is correct
28 Correct 0 ms 340 KB Output is correct
29 Correct 1 ms 468 KB Output is correct
30 Correct 0 ms 468 KB Output is correct
31 Correct 0 ms 340 KB Output is correct
32 Correct 0 ms 468 KB Output is correct
33 Correct 0 ms 340 KB Output is correct
34 Correct 0 ms 340 KB Output is correct
35 Correct 0 ms 212 KB Output is correct
36 Correct 0 ms 340 KB Output is correct
37 Correct 0 ms 340 KB Output is correct
38 Correct 1 ms 468 KB Output is correct
39 Correct 0 ms 468 KB Output is correct
40 Correct 1 ms 468 KB Output is correct
41 Correct 1 ms 468 KB Output is correct
42 Correct 1 ms 468 KB Output is correct
43 Correct 1 ms 468 KB Output is correct
44 Correct 1 ms 468 KB Output is correct
45 Correct 1 ms 468 KB Output is correct
46 Correct 1 ms 468 KB Output is correct
47 Correct 1 ms 468 KB Output is correct
48 Correct 1 ms 468 KB Output is correct
49 Correct 1 ms 468 KB Output is correct
50 Correct 0 ms 468 KB Output is correct
51 Correct 0 ms 212 KB Output is correct
52 Correct 0 ms 340 KB Output is correct
53 Correct 0 ms 340 KB Output is correct
54 Correct 1 ms 340 KB Output is correct
55 Correct 1 ms 340 KB Output is correct
56 Correct 0 ms 468 KB Output is correct
57 Correct 1 ms 980 KB Output is correct
58 Correct 2 ms 2260 KB Output is correct
59 Correct 3 ms 2260 KB Output is correct
60 Correct 3 ms 2260 KB Output is correct
61 Correct 3 ms 2260 KB Output is correct
62 Correct 3 ms 2260 KB Output is correct
63 Correct 3 ms 2260 KB Output is correct
64 Correct 4 ms 2152 KB Output is correct
65 Correct 13 ms 2224 KB Output is correct
66 Correct 8 ms 2260 KB Output is correct
67 Correct 5 ms 2260 KB Output is correct
68 Correct 4 ms 2260 KB Output is correct
69 Correct 4 ms 2260 KB Output is correct
70 Correct 4 ms 2260 KB Output is correct
71 Correct 12 ms 5460 KB Output is correct
72 Correct 38 ms 16332 KB Output is correct
73 Correct 60 ms 16244 KB Output is correct
74 Correct 65 ms 16256 KB Output is correct
75 Correct 67 ms 16224 KB Output is correct
76 Correct 70 ms 16244 KB Output is correct
77 Correct 61 ms 16248 KB Output is correct
78 Correct 68 ms 16212 KB Output is correct
79 Correct 46 ms 16252 KB Output is correct
80 Correct 65 ms 16248 KB Output is correct
81 Correct 67 ms 16248 KB Output is correct
82 Correct 70 ms 16248 KB Output is correct
83 Correct 66 ms 16252 KB Output is correct
84 Correct 59 ms 16248 KB Output is correct
85 Correct 162 ms 32696 KB Output is correct
86 Correct 436 ms 69472 KB Output is correct
87 Correct 380 ms 69476 KB Output is correct
88 Correct 443 ms 69452 KB Output is correct
89 Correct 373 ms 69476 KB Output is correct
90 Correct 414 ms 69416 KB Output is correct
91 Correct 451 ms 69576 KB Output is correct
92 Correct 452 ms 69476 KB Output is correct
93 Correct 410 ms 69476 KB Output is correct
94 Correct 436 ms 69472 KB Output is correct
95 Correct 490 ms 69480 KB Output is correct
96 Correct 488 ms 69476 KB Output is correct
97 Correct 393 ms 69472 KB Output is correct