/* -*- coding: utf-8 -*- * * 3735.cc: No.3735 Offbeat Permutation Tree - yukicoder */ #include #include #include #include #include #include #include using namespace std; /* constant */ const int MAX_N = 500; const int MAX_NN = MAX_N * MAX_N; /* typedef */ using pii = pair; using mpii = map; using tp3 = tuple; using vtp3 = vector; struct UFT { vector links, ranks, sizes; UFT() {} void init(int n) { links.resize(n); for (int i = 0; i < n; i++) links[i] = i; ranks.assign(n, 1); sizes.assign(n, 1); } int root(int i) { int i0 = i; while (links[i0] != i0) i0 = links[i0]; return (links[i] = i0); } int rank(int i) { return ranks[root(i)]; } int size(int i) { return sizes[root(i)]; } bool same(int i, int j) { return root(i) == root(j); } int merge(int i0, int i1) { int r0 = root(i0), r1 = root(i1), mr; if (r0 == r1) return r0; if (ranks[r0] == ranks[r1]) { links[r1] = r0; sizes[r0] += sizes[r1]; ranks[r0]++; mr = r0; } else if (ranks[r0] > ranks[r1]) { links[r1] = r0; sizes[r0] += sizes[r1]; mr = r0; } else { links[r0] = r1; sizes[r1] += sizes[r0]; mr = r1; } return mr; } }; /* global variables */ /* n=4: +-o +-+ | | | +-+-+ o | o +-+-+ | | | +-+ o-+ */ const tp3 gn4[15] = { {0, 0, 0}, {0, 2, 0}, {1, 0, 0}, {1, 1, 0}, {2, 1, 0}, {2, 2, 0}, {3, 0, 0}, {3, 2, 0}, {0, 0, 1}, {0, 2, 1}, {0, 3, 1}, {1, 2, 1}, {2, 0, 1}, {2, 1, 1}, {2, 3, 1}, }; /* n=5: +-+-+-+-o | +-o +-+-+ | | | +-+-+ o-+ | o +-+-+-+ | | | +-+ o-+-+ */ const tp3 gn5[24] = { {0, 0, 0}, {0, 1, 0}, {0, 2, 0}, {0, 3, 0}, {1, 0, 0}, {1, 2, 0}, {1, 3, 0}, {2, 0, 0}, {2, 1, 0}, {2, 3, 0}, {3, 1, 0}, {3, 2, 0}, {3, 3, 0}, {4, 0, 0}, {4, 2, 0}, {4, 3, 0}, {0, 0, 1}, {1, 0, 1}, {1, 2, 1}, {1, 4, 1}, {2, 2, 1}, {3, 0, 1}, {3, 1, 1}, {3, 4, 1}, }; /* subroutines */ void addedge(vtp3 &es, mpii &dgs, const int uy, const int ux, const int di) { es.push_back({uy, ux, di}); int vy = uy + di, vx = ux + (di ^ 1); dgs[{uy, ux}]++; dgs[{vy, vx}]++; } void addedge(vtp3 &es, mpii &dgs, const tp3 &e) { addedge(es, dgs, get<0>(e), get<1>(e), get<2>(e)); } bool check(int n, vtp3 &es, mpii &dgs, int miny) { bool hcs[MAX_N] = {}, vcs[MAX_N] = {}; for (auto &[p, d]: dgs) if (d == 1) { auto [y, x] = p; y -= miny; if (hcs[y] || vcs[x]) return false; hcs[y] = vcs[x] = true; } int nn = n * n; UFT uft; uft.init(nn); for (auto [uy, ux, di]: es) { uy -= miny; int u = uy * n + ux; int vy = uy + di, vx = ux + (di ^ 1), v = vy * n + vx; if (uft.same(u, v)) return false; uft.merge(u, v); } return (uft.size(0) == nn); } /* main */ int main() { int n; scanf("%d", &n); if (n <= 3) { puts("-1"); return 0; } int m = 4 + (n & 1); int gen = m * m - 1; const auto &gn = (m == 4) ? gn4 : gn5; vtp3 es; mpii dgs; for (int i = 0; i < gen; i++) addedge(es, dgs, gn[i]); int miny = 0, maxy = m - 1; while (m < n) { if (dgs[{maxy, m - 1}] > 1) { // expand to right-down addedge(es, dgs, maxy + 1, m, 1); for (int x = m - 1; x >= 0; x--) addedge(es, dgs, maxy + 2, x, 0); addedge(es, dgs, maxy + 1, 0, 1); for (int x = 0; x < m - 1; x++) addedge(es, dgs, maxy + 1, x, 0); addedge(es, dgs, maxy, m - 1, 1); for (int y = maxy + 1; y >= miny; y--) addedge(es, dgs, y, m + 1, 1); addedge(es, dgs, miny, m, 0); for (int y = miny; y < maxy; y++) addedge(es, dgs, y, m, 1); addedge(es, dgs, maxy, m - 1, 0); maxy += 2; } else { // expand to right-up addedge(es, dgs, miny - 2, m, 1); for (int x = m - 1; x >= 0; x--) addedge(es, dgs, miny - 2, x, 0); addedge(es, dgs, miny - 2, 0, 1); for (int x = 0; x < m - 1; x++) addedge(es, dgs, miny - 1, x, 0); addedge(es, dgs, miny - 1, m - 1, 1); for (int y = miny - 2; y < maxy; y++) addedge(es, dgs, y, m + 1, 1); addedge(es, dgs, maxy, m, 0); for (int y = maxy - 1; y >= miny; y--) addedge(es, dgs, y, m, 1); addedge(es, dgs, miny, m - 1, 0); miny -= 2; } m += 2; } for (auto [uy, ux, di]: es) { uy -= miny; int u = uy * n + ux; int vy = uy + di, vx = ux + (di ^ 1), v = vy * n + vx; if (u > v) swap(u, v); printf("%d %d\n", u + 1, v + 1); } //assert(check(n, es, dgs, miny)); return 0; }