#include #define rep(i,n) for(int i = 0; i < (n); ++i) #define rep1(i,n) for(int i = 1; i <= (n); ++i) #define drep(i,n) for(int i = (n)-1; i >= 0; --i) #define srep(i,s,t) for (int i = s; i < (t); ++i) #define rng(a) a.begin(),a.end() #define rrng(a) a.rbegin(),a.rend() #define fi first #define se second #define pb push_back #define eb emplace_back #define em emplace #define pob pop_back #define sz(x) (int)(x).size() #define pcnt __builtin_popcountll #define snuke srand((unsigned)clock()+(unsigned)time(NULL)); #define newline puts("") #define vc vector using namespace std; template using vv = vc>; template using PQ = priority_queue,greater>; using uint = unsigned; using ull = unsigned long long; using vi = vc; using vvi = vv; using vvvi = vv; using ll = long long; using vl = vc; using vvl = vv; using vvvl = vv; using P = pair; using vp = vc

; using vvp = vv

; using LP = pair; int geti(){int x;cin>>x;return x;} vi pm(int n, int s=0) { vi a(n); iota(rng(a),s); return a;} templateistream& operator>>(istream&i,pair&v){return i>>v.fi>>v.se;} templateostream& operator<<(ostream&o,const pair&v){return o<istream& operator>>(istream&i,vc&v){rep(j,sz(v))i>>v[j];return i;} templatestring join(const T&v,const string&d=""){stringstream s;rep(i,sz(v))(i?s<ostream& operator<<(ostream&o,const vc&v){if(sz(v))o<ostream& operator<<(ostream&o,const vv&v){for(auto&r:v)o<void vin(vc&a){int n;cin>>n;a=vc(n);cin>>a;} templatevoid vin(vv&a){int n,m;cin>>n>>m;a=vv(n,vc(m));cin>>a;} templatevoid operator--(pair&a,int){a.fi--;a.se--;} templatevoid operator++(pair&a,int){a.fi++;a.se++;} templatevoid operator--(vc&a,int){for(T&x:a)x--;} templatevoid operator++(vc&a,int){for(T&x:a)x++;} templatepairoperator+(const pair&a,const pair&b){return {a.fi+b.fi,a.se+b.se};} templatepairoperator-(const pair&a,const pair&b){return {a.fi-b.fi,a.se-b.se};} templatepairoperator*(const pair&a,const pair&b){return {a.fi*b.fi,a.se*b.se};} templatepairoperator*(const pair&a,T b){return {a.fi*b,a.se*b};} templatevoid operator+=(pair&a,const pair&b){a.fi+=b.fi;a.se+=b.se;} templatevoid operator-=(pair&a,const pair&b){a.fi-=b.fi;a.se-=b.se;} templatevoid operator*=(pair&a,const pair&b){a.fi*=b.fi;a.se*=b.se;} templatevoid operator*=(pair&a,T b){a.fi*=b;a.se*=b;} templatevoid operator+=(vc&a,T2 b){for(T1&x:a)x+=b;} templatevoid operator-=(vc&a,T2 b){for(T1&x:a)x-=b;} templatevoid operator*=(vc&a,T2 b){for(T1&x:a)x*=b;} templatevoid operator/=(vc&a,T2 b){for(T1&x:a)x/=b;} templatevoid operator%=(vc&a,T2 b){for(T1&x:a)x%=b;} templatevoid operator+=(vc&a,const vc&b){a.insert(a.end(),rng(b));} templatebool mins(T1& x,const T2&y){if(ybool maxs(T1& x,const T2&y){if(xT min(const vc&a){return *min_element(rng(a));} templateT max(const vc&a){return *max_element(rng(a));} templateTx dup(Tx x, Ty y){return (x+y-1)/y;} templatell suma(const vc&a){ll s=0;for(auto&&x:a)s+=x;return s;} templatell suma(const vv&a){ll s=0;for(auto&&x:a)s+=suma(x);return s;} templatevoid uni(T&a){sort(rng(a));a.erase(unique(rng(a)),a.end());} templatevoid prepend(vc&a,const T2&x){a.insert(a.begin(),x);} const double eps = 1e-10; const ll LINF = 1001002003004005006ll; const int INF = 1001001001; #define dame { cout<<"-1"<<'\n'; return;} #define yes { cout<<"Yes"<<'\n'; return;} #define ye { cout<<"Yes"<<'\n';} #define no { cout<<"No"<<'\n'; return;} #define yn {cout<<"Yes"<<'\n';}else{cout<<"No"<<'\n';} #define rtn(x) { cout<<(x)<<'\n'; return;} // flush! #define endl '\n' using vs = vc; void vin(vs& s){int n,m;cin>>n>>m;s=vs(n);cin>>s;} templatevoid rot(T& a,int i){rotate(a.begin(),a.begin()+(i),a.end());} templatevoid rot(vc& a){int h=sz(a),w=sz(a[0]);vc p(w,T(h,0));swap(a,p);rep(i,h)rep(j,w)a[j][h-1-i]=p[i][j];} // maximize static const int N = 128; using bs = bitset; struct BitVector { vc d, mask; BitVector():d(N),mask(N) {} bs sol(bs& b) { bs m; rep(i,N) if (b[i]) { b ^= d[i]; m ^= mask[i]; } return m; } void add(bs b, int id) { bs m = sol(b); m[id] = 1; rep(i,N) if (b[i]) { d[i] = b; mask[i] = m; rep(j,N) if (i != j && d[j][i]) { d[j] ^= b; mask[j] ^= m; } return; } } }; struct Solver { void solve() { int n; cin>>n; vs s(n); cin>>s; vvi a(n,vi(n)); rep(i,n)rep(j,n) a[i][j] = s[i][j]=='#'; vc> ans; auto f = [&](int i, int j, int k, int rots=0) { rep(l,k*2+1) a[i-k+l][j-k+l] ^= 1; rep(l,k*2+1) a[i+k-l][j-k+l] ^= 1; a[i][j] ^= 1; rep(ri,4-rots) { swap(i,j); j = n-1-j; } ans.eb(k,i+1,j+1); }; if (n < 12) { BitVector d; vvi id(n,vi(n)); rep(i,n)rep(j,n) id[i][j] = i*n+j; vc> ts; for (int k = 1; k*2+1 <= n; k++) { srep(i,k,n-k)srep(j,k,n-k) { bs b; rep(l,k*2+1) b.flip(id[i-k+l][j-k+l]); rep(l,k*2+1) b.flip(id[i+k-l][j-k+l]); b.flip(id[i][j]); d.add(b,sz(ts)); ts.eb(i,j,k); } } bs b; rep(i,n)rep(j,n) b[id[i][j]] = a[i][j]; bs m = d.sol(b); if (b.count()) dame; rep(mi,N) if (m[mi]) { auto [i,j,k] = ts[mi]; f(i,j,k); } } else { rep(ri,4) { rep(j,n-2) { if (a[0][j]) f(1,j+1,1,ri); } rot(a); } rep(ri,4) { if (a[1][1]) f(2,2,1,ri); rot(a); } rep(ri,4) { srep(j,2,n-7) { if (a[1][j]) f(2,j+1,1,ri); } for (int j = n-3; j >= n-5; j--) { if (a[1][j]) f(2,j-1,1,ri); } for (int j = n-6; j >= n-7; j--) { if (a[1][j]) { f(1,j+2,1,ri); f(2,j-1,2,ri); f(3,j,3,ri); } } rot(a); } srep(i,2,n-2)srep(j,2,n-2) { if (a[i][j]) { f(i,j,2); for (int di : {-1,1})for(int dj : {-1,1}) f(i+di,j+dj,1); } } } rep(i,n)rep(j,n) if (a[i][j]) dame; { map,int> mp; for (auto t : ans) mp[t] ^= 1; ans.resize(0); for (auto [t,x] : mp) if (x) ans.pb(t); } cout<> ts; rep1(ti,ts) { Solver solver; solver.solve(); } return 0; }