void stableMatching (int n, VVI& maleRank, VVI& femaleRank, VI& wife) {
// a male m prefers w to w' if maleRank[m][w] < maleRank[m][w']
// returns male-optimal matching
VI freeMen;
VVPI fq(n);
VI husband(n, -1);
for (int m = 0; m < n; ++m) {
for (int w = 0; w < n; ++w) {
fq[m].push_back(make_pair(maleRank[m][w], w));
}
sort(all(fq[m]), greater<PI>());
freeMen.push_back(m);
}
while (!freeMen.empty()) {
int m = freeMen.back(), w = fq[m].back().y;
fq[m].pop_back();
if (husband[w] == -1) {
husband[w] = m;
freeMen.pop_back();
} else if (femaleRank[w][m] < femaleRank[w][husband[w]]) {
freeMen.pop_back();
freeMen.push_back(husband[w]);
husband[w] = m;
}
}
wife = VI(n);
for (int w = 0; w < n; ++w) {
wife[husband[w]] = w;
}
}
void DFS (int v) {
idx[v] = index;
low[v] = index;
index += 1;
st.push_back(v);
inStack[v] = true;
for (auto w : adj[v]) {
if (idx[w] == -1) {
DFS(w);
low[v] = min(low[v], low[w]);
} else if (inStack[w]) {
low[v] = min(low[v], low[w]);
}
}
if (low[v] == idx[v]) {
int w;
components.push_back(VI());
do {
w = st.back();
st.pop_back();
inStack[w] = false;
componentOf[w] = totalComponents;
components[totalComponents].push_back(w);
} while (w != v);
totalComponents++;
}
}
bool solve(int n, int k) {
if (k == 1)
return true;
if (k > MAXK)
return false;
if (fact[k] > n)
return false;
VI v;
int N = n;
for (VI::iterator it = primes.begin(); it != primes.end() && (*it) * (*it) <= N; ++it)
if (N % *it == 0) {
v.push_back(0);
while (N % *it == 0) {
++v.back();
N /= *it;
}
}
if (N > 1)
v.push_back(1);
sort(v.begin(), v.end());
reverse(v.begin(), v.end());
k -= (int) v.size() + 1;
for (VI::iterator it = v.begin(); it != v.end(); ++it)
*it -= 1;
while (!v.empty() && v.back() == 0) {
v.pop_back();
}
if (k <= 0)
return true;
if (DBG + 0) {
cerr << "BEGIN!!!!!\n";
for (VI::iterator it = v.begin(); it != v.end(); ++it)
cerr << *it << " -- ";
cerr << endl;
cerr << k << endl;
}
VI w(v.size(), 1);
bool found = walk1(v, w, 0, k/*,set<VI>()*/);
if (!found) {
if (v.size() >= 3 && v[2] >= 3) {
v[0] -= 1;
v[1] -= 1;
v[2] -= 1;
found = walk1(v, w, 0, k - 1/*,set<VI>()*/);
}
}
return found;
}
pii minimum_odd()
{
pii ret(-1,-1);
if(!ones.empty()){
ret = pii(1,ones.back());
ones.pop_back();
}
else
if(!odd.empty())
{
ret = odd.top();
odd.pop();
}
return ret;
}
void dfs(int depth, VI& nums, VI& cur, USET_VI& uset, VVI& result) {
if (depth == nums.size()) {
if (check(cur)) {
string s = toString(cur);
if (uset.find(s) == uset.end()) {
uset.insert(s);
result.push_back(cur);
}
}
}
else {
dfs(depth + 1, nums, cur, uset, result);
cur.push_back(nums[depth]);
dfs(depth + 1, nums, cur, uset, result);
cur.pop_back();
}
}
void DFS(){
visited.resize(k,0);
REP(v,k) if (!visited[v]){
visited[v] = 1;
printf("%d 0\n",v+1);
stack.PB(v);
while (!(stack.empty())){
int u = stack.back();
stack.pop_back();
for(auto ngb : sol[u])
if (!visited[ngb]){
visited[ngb] = 1;
printf("%d %d\n",ngb+1,u+1);
stack.PB(ngb);
}
}
}
}
void dfs(int u,int l){
vs[u] = 1;
d[u] = l;
v.PB(u);
for(int i=0;i<SZ(g[u]);i++){
int w = g[u][i];
if(!vs[w]){
p[w] = u;
dfs(w,l+1);
}
else{
if(w!=p[u]){
for(int j=d[w];j<SZ(v);j++){
m[v[j]] = 1;
}
}
}
}
v.pop_back();
}
int f(VI Q, VI R) {
int rem=0;
while(SZ(Q)<SZ(R)) Q.push_back(0);
while(SZ(Q)>SZ(R)) rem+=Q.back(), Q.pop_back();
assert(SZ(Q)==SZ(R));
int debt=0;
REP(i,SZ(R)) {
if(R[i]>Q[i]) {
debt+=R[i]-Q[i];
continue;
}
if(R[i]<Q[i]) {
rem+=Q[i]-R[i];
}
}
return debt>rem?Inf:debt;
}
int DFS (PI v, int index) {
idx[v.x] = index;
low[v.x] = index;
index += 1;
int children = 0;
bool ap = false;
for (auto w : adj[v.x]) if (w.y != v.y) {
if (idx[w.x] == -1) {
st.push_back(w.y);
index = DFS(w, index);
low[v.x] = min(low[v.x], low[w.x]);
if (low[w.x] > idx[v.x]) {
bridges.push_back(w.y);
}
children++;
if (low[w.x] >= idx[v.x]) {
if (v.y != -1 || children >= 2) {
ap = true;
}
components.push_back(VI());
totalComponents++;
int u;
do {
u = st.back();
st.pop_back();
components.back().push_back(u);
} while (u != w.y);
}
} else if (idx[w.x] < idx[v.x]) {
st.push_back(w.y);
low[v.x] = min(low[v.x], idx[w.x]);
}
}
if (ap) {
cutVertices.push_back(v.x);
}
return index;
}
int minValue(int N, int K, vector <int> s) {
int m = SZ(s);
int sum = 0;
REP(i, m) sum += s[i];
if (sum <= (K - 1) * N) return 0;
else {
int tot = N;
int ans = 0;
VI q;
REP(i, m) if (s[i]) q.push_back(s[i]);
sort(ALL(q));
reverse(ALL(q));
while (sum > (K - 1) * N && N > 0) {
sum -= SZ(q);
REP(i, SZ(q)) q[i]--;
while (SZ(q) && q.back() == 0) q.pop_back();
N--;
ans++;
}
return ans;
}
}