C - 部門分け AtCoder Regular Contest 056

C - 部門分け

o(n ^ 3)で部分集合が列挙できる
いくつかの集合に分けるため、それらの評価値を独立して考えたい
部分問題として考えるには
dp[m] := 全体の集合がmとした時の問いの答えとすればいい
遷移はdp[m] = dp[s] + dp[m-s] - 二つの間の信頼値の合計となる
上は集合m内での信頼値の合計から集合sでの合計、集合m-sでの合計を引けば求まる

> |c++|
//MLEが動かない
//セグフォは関数内で要素のでかい配列を定義しているから
//todo　idef DEBUGで、境界チェック付きのvectorを作りたい
//http://marycore.jp/prog/cpp/class-extension-methods/
//現状ifdef DEBUG が何故か動かないので出来ない

#include

using namespace std;
#define int long long
#define ll long long
#define double long double

struct initon {
initon() {
cin.tie(0);
ios::sync_with_stdio(false);
cout.setf(ios::fixed);
cout.precision(16);
};
} hoee;

namespace std {
template<>
class hash> {
public:
size_t operator()(const std::pair &x) const {
return hash()(((ll) x.first << 32) + x.second);
}
};

template<>
class hash> {
public:
size_t operator()(const std::pair &x) const {
return hash()(((ll) x.first << 32) + x.second);
}
};
}
struct Tri {
int f, s, t;

Tri() {
f = -1, s = -1, t = -1;
}

Tri(int f, int s, int t) : f(f), s(s), t(t) {}

bool operator<(const Tri &r) const {
return f != r.f ? f < r.f : s != r.s ? s < r.s : t < r.t;
//return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 大きい順
}

bool operator>(const Tri &r) const {
return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t;
//return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 小さい順
}

int operator(int i) {
assert(i < 3);
switch (i) {
case 0:
return f;
break;
case 1:
return s;
break;
default:
return t;
break;
}
}
};

template
istream &operator>>(istream &is, vector &vec) {
for (T &x: vec) is >> x;
return is;
}

template
ostream &operator<<(ostream &os, vector &vec) {
for (int i = 0; i < vec.size(); i++) {
os << vec[i] << (i + 1 == vec.size() ? "" : " ");
}
return os;
}

template
void resize(vector &vec, const H head) { //再帰の終端。 可変長templateの長さが 0 になるとこっちが呼ばれる。
vec.resize(head);
}

template
void resize(vector &vec, const H &head, const T ... tail) {
vec.resize(head);
for (auto &v: vec) resize(v, tail...);
}

//別n名
#define ull unsigned long long
#define vec vector
#define con continue
#define bre break
#define brk break
#define is ==
#define eq ==
#define no !=
#define ne !=
#define dif !=
#define df !=
#define rs resize
#define PQ priority_queue, greater >
using seti = set;
using vi = vector;
#define vvi(a, b, c) vec a(b,vi(c))
using vb = vector;
#define vvb(a, b, c) vec a(b,vb(c))
using vs = vector;
#define vvs(a, b, c) vec a(b,vs(c))
using vl = vector;
#define vvl(a, b, c) vec a(b,vl(c))
using vd = vector;
#define vvd(a, b, c) vec a(b,vd(c))
#define v3i(a, b, c, d) vector> a(b, vector(c, vi(d)))
#define v3d(a, b, c, d) vector> a(b, vector(c, vd(d)))
#define v3m(a, b, c, d) vector> a(b, vector(c, vm(d)))
using vc=vector;
#define vvc(a, b, c) vec a(b,vc(c))
using P = pair;
//using T = tuple;
using vp = vector

;
#define vvp(a, b, c) vec a(b,vp(c))
using vt = vector;
#define vvt(a, b, c) vec a(b,vt(c))
using dou = double;
using itn = int;
using str = string;
using bo= bool;
#define uset unordered_set
#define mset multiset
#define umap unordered_map
#define mmap multimap
#define F first
#define S second

//定数
#define k4 10101
#define k5 101010
#define k6 1010101
#define k7 10101010

const int inf = (int) 1e9 + 100;
const ll linf = (ll) 1e18 + 100;
const double eps = 1e-9;
const int y4 = {-1, 1, 0, 0};
const int x4 = {0, 0, -1, 1};
const int y8 = {0, 1, 0, -1, -1, 1, 1, -1};
const int x8 = {1, 0, -1, 0, 1, -1, 1, -1};

//配列
#define sz(a) (sizeof(a)/sizeof(a[0]))

//コンテナ
#define mp make_pair
#define pb push_back
#define pf push_front
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()

template
T pop(set &set) {
T res = *set.begin();
set.erase(set.find(res));
return res;
}

template
T pop(mset &set) {
T res = *set.begin();
set.erase(set.find(res));
return res;
}

template
T popBack(set &set) {
T res = *set.rbegin();
set.erase(set.find(res));
return res;
}

template
T popBack(mset &set) {
T res = *set.rbegin();
set.erase(set.find(res));
return res;
}

template
inline void sort(vector &a) { sort(a.begin(), a.end()); };

template
inline void rsort(vector &a) { sort(a.begin(), a.end(), greater()); };

template
inline void sort(vector &a, int len) { sort(a.begin(), a.begin() + len); };

template
inline void rsort(vector &a, int len) { sort(a.begin(), a.begin() + len, greater()); };

template
inline void sort2(vector> &a) {
int n = a.size();
for (int i = 0; i < n; i++) {
sort(a[i]);
}
}

template
inline void rsort2(vector> &a) {
int n = a.size();
for (int i = 0; i < n; i++) {
rsort(a[i]);
}
}

//繰り返し
#define _overloadrep(_1, _2, _3, name, ...) name
# define _rep(i, n) for(int i = 0; i < n ; i++)
#define repi(i, m, n) for(int i = m; i < n ; i++)
#define rep(...) _overloadrep(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)
#define _rer(i, n) for(int i = n; i >= 0 ; i--)
#define reri(i, m, n) for(int i = m; i >= n ; i--)
#define rer(...) _overloadrep(__VA_ARGS__,reri,_rer,)(__VA_ARGS__)
#define fora(a, b) for(auto&& a : b)
#define forr(a, b) for_each(map.rbegin(),map.rend(),(auto&& a)
#define rea(a, b) for(auto&& a : b)
#define repa(a, b) for(auto&& a : b)

template
void fill(A (&a)[N], const T &v) {
rep(i, N)a[i] = v;
}

template
void fill(A (&a)[N][O], const T &v) {
rep(i, N)rep(j, O)a[i][j] = v;
}

template
void fill(A (&a)[N][O][P], const T &v) {
rep(i, N)rep(j, O)rep(k, P)a[i][j][k] = v;
}

template
void fill(A (&a)[N][O][P][Q], const T &v) {
rep(i, N)rep(j, O)rep(k, P)rep(l, Q)a[i][j][k][l] = v;
}

template
void fill(A (&a)[N][O][P][Q][R], const T &v) {
rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)a[i][j][k][l][m] = v;
}

template
void fill(A (&a)[N][O][P][Q][R][S], const T &v) {
rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)rep(n, S)a[i][j][k][l][m][n] = v;
}

template
void fill(vector &a, U v) {
rep(i, a.size())a[i] = v;
}

template
void fill(vector> &a, U v) {
rep(i, a.size())rep(j, a[0].size())a[i][j] = v;
}

template
void fill(vector>> &a, U v) {
rep(i, a.size())rep(j, a[0].size())rep(k, a[0][0].size())a[i][j][k] = v;
}

#define arcpy(a, b) memcpy(a,b,sizeof(b))

//入力
template
T in() {
T x;
cin >> x;
return (x);
}

string sin() { return in(); }

double din() { return in(); }

ll lin() { return in(); }

#define na(a, n) rep(i,n) cin >> a[i];
#define nad(a, n) rep(i,n) cin >> a[i], a[i]--;
#define na3(a, b, c, n) rep(i, n)cin >> a[i] >> b[i] >> c[i];
#define add2(a, b, n) rep(i, n)a.pb(in()),b.pb(in());
#define add2d(a, b, n) rep(i, n)a.pb(in()-1),b.pb(in()-1);
#define add3(a, b, c, n) rep(i, n)a.pb(in()),b.pb(in()),c.pb(in());
#define add3d(a, b, c, n) rep(i, n)a.pb(in()-1),b.pb(in()-1),c.pb(in());
#define na2(a, b, n) rep(i, n)cin >> a[i] >> b[i];

#define nt(a, h, w) rep(hi,h)rep(wi,w) cin >> a[hi][wi];
#define ntd(a, h, w) rep(hi,h)rep(wi,w) cin >> a[hi][wi], a[hi][wi]--;
#define ntp(a, h, w) fill(a,'#');rep(hi,1,h+1)rep(wi,1,w+1) cin >> a[hi][wi];

#define addn(a, n) a.resize(n);na(a,n);
#define addnd(a, n) a.resize(n);na(a,n);rep(i,n)a[i]--;

//出力
template
void out(vector x) {
for (auto &&v : x) cout << v << " ";
cout << "" << endl;
}

template
void out(T x) {
if (typeid(x) == typeid(double))cout << fixed << setprecision(10) << x << endl;
else cout << x << endl;
}
//デバッグ
#define debug(x) cerr << x << " " << "(L:" << __LINE__ << ")" << '\n';
// 境界チェック付きvector
namespace std_vector_bounds_checking {
using namespace std;

template>
struct vector : std::vector {
using std::vector::vector;

typename std::vector::reference operator(typename std::vector::size_type n) {
return this->at(n);
}
};
}
//よく使うクラス、構造体
class UnionFind {
public:
vi par, rank, sizes;
int n, trees;

UnionFind(int n) : n(n), trees(n) {
par.resize(n), rank.resize(n), sizes.resize(n);
rep(i, n)par[i] = i, sizes[i] = 1;
}

int root(int x) {
if (par[x] == x)return x;
else return par[x] = root(par[x]);
}

void unite(int x, int y) {
x = root(x);
y = root(y);
if (x == y)return;
if (rank[x] < rank[y])swap(x, y);
trees--;
par[y] = x;
sizes[x] += sizes[y];
if (rank[x] == rank[y])rank[x]++;
}

bool same(int x, int y) { return root(x) == root(y); }

int size(int x) { return sizes[root(x)]; }
//順不同 umapなので
vec sets() {
vec res(trees);
umap map;
rep(i, n) map[root(i)].push_back(i);
int i = 0;
for (auto &&p:map) {
int r = p.F;
res[i].push_back(r);
for (auto &&v:p.S) {
if (r == v)continue;
res[i].push_back(v);
}
i++;
}
return res;
}
};

//MOD関連
ll MOD = (int) 1e9 + 7;

int mpow(int v, ll a) {
ll x = v, n = a, res = 1;
while (n) {
if (n & 1)res = (res * x) % MOD;
x = (x * x) % MOD;
n >>= 1;
}
return res;
}

class mint {
private:
ll v;
public:
static ll mod(ll a) { return (a % MOD + MOD) % MOD; }

mint(ll a = 0) { this->v = mod(a); };

mint(const mint &a) { v = a.v; }

mint operator+(const mint &a) { return mint(v + a.v); }

mint operator+(const ll a) { return mint(v + a % MOD); }

mint operator+(const signed a) { return mint(v + a % MOD); }

friend mint operator+(const ll a, const mint &b) { return mint(a % MOD + b.v); }

void operator+=(const mint &a) { v = (v + a.v) % MOD; }

void operator+=(const ll a) { v = mod(v + a % MOD); }

void operator+=(const signed a) { v = mod(v + a % MOD); }

friend void operator+=(ll &a, const mint &b) { a = mod(a % MOD + b.v); }

mint operator-(const mint &a) { return mint(v - a.v); }

mint operator-(const ll a) { return mint(v - a % MOD); }

mint operator-(const signed a) { return mint(v - a % MOD); }

friend mint operator-(const ll a, const mint &b) { return mint(a % MOD - b.v); }

void operator-=(const mint &a) { v = mod(v - a.v); }

void operator-=(const ll a) { v = mod(v - a % MOD); }

void operator-=(const signed a) { v = mod(v - a % MOD); }

friend void operator-=(ll &a, const mint &b) { a = mod(a % MOD - b.v); }

mint operator*(const mint &a) { return mint(v * a.v); }

mint operator*(const ll a) { return mint(v * (a % MOD)); }

mint operator*(const signed a) { return mint(v * (a % MOD)); }

friend mint operator*(const ll a, const mint &b) { return mint(a % MOD * b.v); }

void operator*=(const mint &a) { v = (v * a.v) % MOD; }

void operator*=(const ll a) { v = mod(v * (a % MOD)); }

void operator*=(const signed a) { v = mod(v * (a % MOD)); }

friend void operator*=(ll &a, const mint &b) { a = mod(a % MOD * b.v); }

mint operator/(const mint &a);

mint operator/(const ll a);

mint operator/(const signed a);

friend mint operator/(const ll a, const mint &b);

void operator/=(const mint &a);

void operator/=(const ll a);

void operator/=(const signed a);

friend void operator/=(ll &a, const mint &b);

mint operator^(const mint &a) { return mpow(v, a.v); };

mint operator^(const ll a) { return mpow(v, a); };

mint operator^(const signed a) { return mpow(v, a); };

friend mint operator^(const ll a, const mint &b) { return mpow(a, b.v); };

void operator^=(const mint &a) { v = mpow(v, a.v); }

void operator^=(const ll a) { v = mpow(v, a); }

void operator^=(const signed a) { v = mpow(v, a); }

//単項演算子
mint operator+() { return *this; }

mint operator++() {
v++;
return *this;
}

mint operator++(signed d) {
mint res = *this;
v++;
return res;
}

mint operator-() { return operator*(-1); }

mint operator--() {
v++;
return *this;
}

void operator--(signed d) {
mint res = *this;
v++;
}

bool operator==(mint &a) {
return v == a.v;
}

bool operator==(signed a) {
return v == a;
}

friend bool operator==(signed a, mint &b) {
return a == b.v;
}

bool operator!=(mint &a) {
return v != a.v;
}

bool operator!=(signed a) {
return v != a;
}

friend bool operator!=(signed a, mint &b) {
return a != b.v;
}

operator int() { return v; }
};

const int setModMax = 510000;
mint fac[setModMax], finv[setModMax], inv[setModMax];

void setMod() {
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
for (int i = 2; i < setModMax; i++) {
fac[i] = fac[i - 1] * i % MOD;
inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
finv[i] = finv[i - 1] * inv[i] % MOD;
}
}

mint minv(ll a) {
if (fac[0] == 0)setMod();
if (a < setModMax) return inv[a];
a %= MOD;
ll b = MOD, x = 1, y = 0;
while (b) {
ll t = a / b;
a -= t * b;
swap(a, b);
x -= t * y;
swap(x, y);
}
return (x % MOD + MOD) % MOD;
}

mint mint::operator/(const mint &a) { return mint(v * minv(a.v)); }

mint mint::operator/(const ll a) { return mint(v * minv(a)); }

mint mint::operator/(const signed a) { return mint(v * minv(a)); }

mint operator/(const ll a, const mint &b) { return mint(a % MOD * minv(b.v)); }

void mint::operator/=(const mint &a) { v = (v * minv(a.v)) % MOD; }

void mint::operator/=(const ll a) { v = mod(v * minv(a)); }

void mint::operator/=(const signed a) { v = mod(v * minv(a)); }

void operator/=(ll &a, const mint &b) { a = mint::mod(a % MOD * minv(b.v)); }

using vm=vector;
#define vvm(a, b, c) vec a(b,vm(c))
bool isPrime[4010101];
vi primes;

void setPrime() {
fill(isPrime, true);
isPrime[0] = isPrime[1] = false;
for (int i = 2; i <= sqrt(sz(isPrime)) + 5; ++i) {
if (!isPrime[i])continue;
for (int j = 2; i * j < sz(isPrime); ++j) {
isPrime[i * j] = false;
}
}
rep(i, sz(isPrime))if (isPrime[i])primes.pb(i);
}

mint com(ll n, ll r) {
if (n < r || n < 0 || r < 0)return 0;
if (fac[0] == 0)setMod();
return fac[n] * (finv[r] * finv[n - r] % MOD) % MOD;
}

//便利関数
void OLE() {
string a = "a";
rep(i, 30)a += a;
rep(i, 1 << 17)cout << a << endl;
cout << "OLE 出力長制限超過" << endl;
exit(0);
}

void TLE() {
int a = 1;
while (a)cout << a << endl;
}

void RE() {
int a = 1 / (x4[0] / MOD);
cout << a << endl;
}

ll gcd(ll a, ll b) {
return b ? gcd(b, a % b) : a;
}

ll lcm(ll a, ll b) {
return a / gcd(a, b) * b;
}

bool equal(double a, double b) {
return fabs(a - b) < eps;
}

ll reverse(ll a) {
ll res = 0;
while (a) {
res *= 10;
res += a % 10;
a /= 10;
}
return res;
}

ll ceil(ll a, ll b) {
if (b == 0) {
OLE();
return -1;
} else return (a + b - 1) / b;
}

ll sqrt(ll a) {
if (a < 0)OLE();
ll res = (ll) std::sqrt(a);
while (res * res < a)res++;
return res;
}

double log(double e, double x) {
return log(x) / log(e);
}

ll sig(ll t) { return (1 + t) * t / 2; }

ll sig(ll s, ll t) { return (s + t) * (t - s + 1) / 2; }

vi divisors(int v) {
vi res;
for (int i = 1; i <= sqrt(v); ++i) {
if (v % i == 0) {
res.pb(i);
if (i != v / i)res.pb(v / i);
}
}
return res;
}

vi factorization(int v) {
int tv = v;
vi res;
if (!isPrime[2])setPrime();
for (auto &&p :primes) {
if (v % p == 0)res.push_back(p);
while (v % p == 0) {
v /= p;
}
if (v == 1 || p * p > tv)break;
}
if (v > 1)res.pb(v);
return res;
}

unordered_map factorizationMap(int v) {
int tv = v;
unordered_map res;
if (!isPrime[2])setPrime();
for (auto &&p :primes) {
while (v % p == 0) {
res[p]++;
v /= p;
}
if (v == 1 || p * p > tv)break;
}
if (v > 1)res[v]++;
return res;
}

int get(int a, int keta) {
a /= (int) pow(10, keta);
return a % 10;
}

int keta(int v) {
int cou = 0;
while (v) {
cou++;
v %= 10;
}
return cou;
}

template
void imo(vector &v) {
int n = v.size();
rep(i, n - 1)v[i + 1] += v[i];
}

//変換系
template
vector keys(map a) {
vector res;
for (auto &&k :a)res.pb(k.F);
return res;
}

template
vector keys(umap a) {
vector res;
for (auto &&k :a)res.pb(k.F);
return res;
}

template
vector values(map a) {
vector res;
for (auto &&k :a)res.pb(k.S);
return res;
}

template
vector values(umap a) {
vector res;
for (auto &&k :a)res.pb(k.S);
return res;
}

vi list(int a) {
vi res;
while (a) {
res.insert(res.begin(), a % 10);
a /= 10;
}
return res;
}

template
bool chmax(T &a, const U &b) {
if (a < b) {
a = b;
return true;
}
return false;
}

template
bool chmin(T &a, const U &b) {
if (b < a) {
a = b;
return true;
}
return false;
}

template
T min(T a, signed b) {
return a < b ? a : b;
}

template
T max(T a, signed b) {
return a < b ? b : a;
}

template
T min(vector a) {
return *min_element(all(a));
}

template
T max(vector a) {
return *max_element(all(a));
}

template
T min(T a) {
T res = a[0];
rep(i, sz(a))chmin(res, a[i]);
return res;
}

template
T max(T a) {
T res = a[0];
rep(i, sz(a))chmax(res, a[i]);
return res;
}

template
T sum(vector &v, int len = -1) {
if (len == -1)len = v.size();
T res = 0;
chmin(len, v.size());
rep(i, len)res += v[i];
return res;
}

template
T sum(vector> &v, int h = -1, int w = -1) {
if (h == -1)h = v.size();
if (w == -1)w = v[0].size();
T res = 0;
chmin(h, v.size());
chmin(w, v[0].size());
rep(i, h)rep(j, w)res += v[i][j];
return res;
}

P sump(vp &v, int len = -1) {
if (len == -1)len = v.size();
P res = {0, 0};
chmin(len, v.size());
rep(i, len) {
res.F += v[i].F;
res.S += v[i].S;
}
return res;
}

///要素が0の時、返り値は0か1か
template
T mul(vector &v, int len = -1) {
if (len == -1)len = v.size();
T res = 1;
chmin(len, v.size());
rep(i, len)res *= v[i];
return res;
}

void clear(PQ &q) {
while (q.size())q.pop();
}

template
void clear(queue &q) {
while (q.size())q.pop();
}

template
vector ruiv(vector &a) {
vector res(a.size() + 1);
rep(i, a.size())res[i + 1] = res[i] + a[i];
return res;
}

template
void plus(vector &a, T v = 1) {
for (auto &&u :a)u += v;
}

template
void minu(vector &a, T v = 1) {
for (auto &&u :a)u -= v;
}

template
void minus(vector &a, T v = 1) {
for (auto &&u :a)u -= v;
}

inline bool inside(int y, int x, int H, int W) { return y >= 0 && x >= 0 && y < H && x < W; }

ll u(ll a) { return a < 0 ? 0 : a; }

#define MIN(a) numeric_limits::min()
#define MAX(a) numeric_limits::max()

template
T min(vector> &a) {
T res = MAX(T);
rep(i, a.size())chmin(res, *min_element(all(a[i])));
return res;
}

template
T max(vector> &a) {
T res = MIN(T);
rep(i, a.size())chmax(res, *max_element(all(a[i])));
return res;
}

bool bget(ll m, int keta) {
return (m >> keta) & 1;
}

int bget(ll m, int keta, int sinsuu) {
m /= (ll) pow(sinsuu, keta);
return m % sinsuu;
}

inline ll bit(int n) {
return (1LL << (n));
}

inline ll bit(int n, int sinsuu) {
return (ll) pow(sinsuu, n);
}

int bcou(ll m) {
return __builtin_popcount(m & 0xFFFFFFFF) + __builtin_popcount(m >> 32);
}
//初期化は0を渡す
ll nextComb(ll &mask, int n, int r) {
if (!mask)return mask = (1LL << r) - 1;
ll x = mask & -mask; //最下位の1
ll y = mask + x; //連続した下の1を繰り上がらせる
ll res = ((mask & ~y) / x >> 1) | y;
if (bget(res, n))return mask = 0;
else return mask = res;
}

//n桁以下でビットがr個立っているもののvectorを返す
vl bitCombList(int n, int r) {
vl res;
int m = 0;
while (nextComb(m, n, r)) {
res.pb(m);
}
return res;
}

int altoi(char c) {
if ('A' <= c && c <= 'Z')return c - 'A';
return c - 'a' + 26;
}

char itoal(int i) {
if (i < 26)return 'A' + i;
return 'a' + i - 26;
}

int ctoi(char c) {
return c - '0';
}

#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

void compress(vi &a) {
vi b;
int len = a.size();
for (int i = 0; i < len; ++i) {
b.push_back(a[i]);
}
sort(b);
UNIQUE(b);
for (int i = 0; i < len; ++i) {
a[i] = lower_bound(all(b), a[i]) - b.begin();
}
}

void compress(int a, int len) {
vi b;
for (int i = 0; i < len; ++i) {
b.push_back(a[i]);
}
sort(b);
UNIQUE(b);
for (int i = 0; i < len; ++i) {
a[i] = lower_bound(all(b), a[i]) - b.begin();
}
}
//要素が見つからなかったときに困る
#define binarySearch(a, v) (binary_search(all(a),v))
#define lowerIndex(a, v) (lower_bound(all(a),v)-a.begin())
#define lowerBound(a, v) (*lower_bound(all(a),v))
#define upperIndex(a, v) (upper_bound(all(a),v)-a.begin())
#define upperBound(a, v) (*upper_bound(all(a),v))
#define ans(a) cout<
inline void fin(T s) { cout << s << endl, exit(0); }

template
struct edge {
int from, to;
T cost;
int id;
int type;

edge(int f, int t, T c = 1, int id = -1, int ty = -1) : from(f), to(t), cost(c), id(id), type(ty) {}

bool operator<(const edge &b) const {
return cost < b.cost;
}

bool operator>(const edge &b) const {
return cost > b.cost;
}
};

template
class graph {
protected:
vector _used;
public :
vector>> g;
vector> edges;
int n, root = -1;

graph(int n) : n(n) {
g.resize(n);
_used.resize(n);
}

void clear() {
g.clear();
edges.clear();
}

void resize(int n) {
this->n = n;
g.resize(n);
_used.resize(n);
}

int size() {
return g.size();
}

bool isleaf(int v) {
assert(root != -1);
return g[v].size() == 1 && g[v][0].from != root;
}

vector > operator[](int i) {
return g[i];
}

virtual void add(int from, int to, T cost, int ty) = 0;

virtual bool used(edge &e) = 0;

virtual bool used(int id) = 0;

virtual void del(edge &e) = 0;

virtual void del(int id) = 0;
};

template
class undigraph : public graph {
public:
using graph::g;
using graph::n;
using graph::edges;
using graph::_used;

undigraph(int n) : graph(n) {
}

void add(int f, int t, T cost = 1, int ty = -1) {
if (!(0 <= f && f < n && 0 <= t && t < n))OLE();
int id = edges.size();
g[f].emplace_back(f, t, cost, id, ty);
g[t].emplace_back(t, f, cost, id + 1, ty);
edges.emplace_back(f, t, cost, id, ty);
edges.emplace_back(t, f, cost, id + 1, ty);
}

void add(edge &e) {
int f = e.from, t = e.to, ty = e.type;
T cost = e.cost;
add(f, t, cost, ty);
}

bool used(edge &e) {
return _used[e.id];
}

bool used(int id) {
return _used[id];
}

void del(edge &e) {
_used[e.id] = _used[e.id ^ 1] = 1;
}

void del(int id) {
_used[id] = _used[id ^ 1] = 1;
}
};

template
class digraph : public graph {
public:
using graph::g;
using graph::n;
using graph::edges;
using graph::_used;

digraph(int n) : graph(n) {
}

void add(int f, int t, T cost = 1, int ty = -1) {
if (!(0 <= f && f < n && 0 <= t && t < n))OLE();
int id = edges.size();
g[f].emplace_back(f, t, cost, ty, id);
edges.emplace_back(f, t, cost, ty, id);
}

bool used(edge &e) {
return _used[e.id];
}

bool used(int id) {
return _used[id];
}

void del(edge &e) {
_used[e.id] = _used[e.id ^ 1] = 1;
}

void del(int id) {
_used[id] = _used[id ^ 1] = 1;
}
};

template
bool nibu(const graph &g) {
UnionFind uf(g.n * 2);
for (auto &&e :g.edges)uf.unite(e.f, e.t + g.n), uf.unite(e.f + g.n, e.t);
return !uf.same(0, g.n);
}

template
vector dijkstra(const graph &g, int s) {
if (!(0 <= s && s < g.n))OLE();
T initValue = MAX(T);
vector dis(g.n, initValue);
priority_queue, vector>, greater>> q;
dis[s] = 0;
q.emplace(0, s);
while (q.size()) {
T nowc = q.top().F;
int i = q.top().S;
q.pop();
if (dis[i] != nowc)continue;
for (auto &&e : g.g[i]) {
int to = e.to;
T cost = nowc + e.cost;
if (dis[to] > cost) {
dis[to] = cost;
q.emplace(dis[to], to);
}
}
}
//たどり着かないなら-1
for (auto &&d :dis) if (d == initValue)d = -1;
return dis;
}

//機能拡張
template
void remove(vector &v, unsigned int i) { v.erase(v.begin() + i); }

template
void remove(vector &v, unsigned int s, unsigned int e) {
v.erase(v.begin() + s, v.begin() + e);
}

template
void removen(vector &v, unsigned int s, unsigned int n) {
v.erase(v.begin() + s, v.begin() + s + n);
}

template
void erase(vector &v, unsigned int i) { v.erase(v.begin() + i); }

template
void erase(vector &v, unsigned int s, unsigned int e) {
v.erase(v.begin() + s, v.begin() + e);
}

template
void erasen(vector &v, unsigned int s, unsigned int n) {
v.erase(v.begin() + s, v.begin() + s + n);
}

template
void insert(vector &v, unsigned int i, T t) { v.insert(v.begin() + i, t); }

template
void insert(vector &v, unsigned int i, vector list) {
for (auto &&va :list)v.insert(v.begin() + i++, va);
}

template
void insert(vector &v, unsigned int i, initializer_list list) {
for (auto &&va :list)v.insert(v.begin() + i++, va);
}

template
void insert(set &v, vector list) {
for (auto &&va :list)v.insert(va);
}

template
void insert(set &v, initializer_list list) {
for (auto &&va :list)v.insert(va);
}

int mod(int a, int m) {
return (a % m + m) % m;
}

ll ma = numeric_limits::min();
ll mi = numeric_limits::max();

//閉路がなければtrue
bool topo(vi &res, digraph g) {
int n = g.g.size();
vi nyu(n);
rep(i, n)for (auto &&e :g[i])nyu[e.to]++;
queue st;
rep(i, n)if (nyu[i] == 0)st.push(i);
while (st.size()) {
int v = st.front();
st.pop();
res.pb(v);
fora(e, g[v]) if (--nyu[e.to] == 0)st.push(e.to);
}
return res.size() == n;
}

//辞書順最小　トポロジカルソート
bool topos(vi &res, digraph g) {
int n = g.g.size();
vi nyu(n);
rep(i, n)for (auto &&e :g[i])nyu[e.to]++;
set st;
rep(i, n)if (nyu[i] == 0)st.insert(i);
while (st.size()) {
int i = *st.begin();
st.erase(st.begin());
res.pb(i);
fora(e, g[i])if (--nyu[e.to] == 0)st.insert(e.to);
}
return res.size() == n;
}

vector split(const string a, const char deli) {
string b = a + deli;
int l = 0, r = 0, n = b.size();
vector res;
rep(i, n) {
if (b[i] == deli) {
r = i;
if (l < r)res.push_back(b.substr(l, r - l));
l = i + 1;
}
}
return res;
}

vector split(const string a, const string deli) {
string b = a + deli;
int l = 0, r = 0, n = b.size(), dn = deli.size();
vector res;
rep(i, n) {
if (i + dn <= n && b.substr(i, i + dn) == deli) {
r = i;
if (l < r)res.push_back(b.substr(l, r - l));
i += dn - 1;
l = i + 1;
}
}
return res;
}

int n, k, m, h, w, x, y, q, r;
int cou;
vvi (a, 22, 22);
vi dp(1 << 22);//考慮店
vi was(1 << 22);
vi tru(1 << 22);

int ds(int m) {
if (was[m])return dp[m];
for (int ms = (m - 1) & m; ms > 0; ms = (ms - 1) & m) {
int minu = tru[m] - tru[ms] - tru[m - ms];
chmax(dp[m], ds(ms) + ds(m - ms) - minu);
}
was[m] = 1;
return dp[m];
}

signed main() {
cin >> n >> k;
nt(a, n, n);
fill(dp, k);
rep(m, 1 << n) {
rep(i, n) {
rep(j, i) {
if ((bget(m, i) && bget(m, j)))tru[m] += a[i][j];
}
}
}
cout << ds((1 << n) - 1) << endl;

return 0;
}