#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template static void amin(T &x, U y) { if (y < x) x = y; } template static void amax(T &x, U y) { if (x < y) x = y; } template, int BlockSize = 10> class DirectRMQ { public: typedef int Index; //今のところ大きくともintを仮定している(queryとか) typedef char InBlockIndex; typedef InBlockIndex(*BlockTypeRef)[BlockSize]; DirectRMQ(Compare comp_ = Compare()) : blockTypes(0), innerBlockTable(0), sparseTable(0) { comp = comp_; calcBallotNumbers(); buildInnerBlockTable(); } ~DirectRMQ() { delete[] innerBlockTable; delete[] blockTypes; delete[] sparseTable; } void build(const Val *a, Index n) { blocks = (n + BlockSize - 1) / BlockSize; stHeight = 0; while (1 << stHeight < blocks) ++ stHeight; delete[] blockTypes; delete[] sparseTable; blockTypes = new BlockTypeRef[blocks]; calcBlockTypes(a, n); buildInnerBlockTable(a, n); sparseTable = new Index[blocks * stHeight]; buildSparseTable(a); } //[l,r]の閉区間 Index query(const Val *a, Index l, Index r) const { Index x = l / BlockSize, y = r / BlockSize, z = y - x; if (z == 0) return x * BlockSize + blockTypes[x][l % BlockSize][r % BlockSize]; if (z == 1) return assumeleft_minIndex(a, x * BlockSize + blockTypes[x][l % BlockSize][BlockSize - 1], y * BlockSize + blockTypes[y][0][r % BlockSize]); z -= 2; Index k = 0, s; s = ((z & 0xffff0000) != 0) << 4; z >>= s; k |= s; s = ((z & 0x0000ff00) != 0) << 3; z >>= s; k |= s; s = ((z & 0x000000f0) != 0) << 2; z >>= s; k |= s; s = ((z & 0x0000000c) != 0) << 1; z >>= s; k |= s; s = ((z & 0x00000002) != 0) << 0; z >>= s; k |= s; return assumeleft_minIndex(a , assumeleft_minIndex(a, x * BlockSize + blockTypes[x][l % BlockSize][BlockSize - 1], sparseTable[x + 1 + blocks * k]) , assumeleft_minIndex(a, sparseTable[y + blocks * k - (1 << k)], y * BlockSize + blockTypes[y][0][r % BlockSize]) ); } Val queryVal(const Val *a, Index l, Index r) const { Index x = l / BlockSize, y = r / BlockSize, z = y - x; if (z == 0) return a[x * BlockSize + blockTypes[x][l % BlockSize][r % BlockSize]]; Val edge = minVal( a[x * BlockSize + blockTypes[x][l % BlockSize][BlockSize - 1]], a[y * BlockSize + blockTypes[y][0][r % BlockSize]]); if (z == 1) return edge; z -= 2; Index k = 0, s; s = ((z & 0xffff0000) != 0) << 4; z >>= s; k |= s; s = ((z & 0x0000ff00) != 0) << 3; z >>= s; k |= s; s = ((z & 0x000000f0) != 0) << 2; z >>= s; k |= s; s = ((z & 0x0000000c) != 0) << 1; z >>= s; k |= s; s = ((z & 0x00000002) != 0) << 0; z >>= s; k |= s; return minVal(edge, minVal( a[sparseTable[x + 1 + blocks * k]], a[sparseTable[y + blocks * k - (1 << k)]])); } private: Compare comp; int ballotNumbers[BlockSize + 1][BlockSize + 1]; InBlockIndex(*innerBlockTable)[BlockSize][BlockSize]; Index blocks; int stHeight; BlockTypeRef *blockTypes; Index *sparseTable; inline Index minIndex(const Val *a, Index x, Index y) const { return comp(a[x], a[y]) || (a[x] == a[y] && x < y) ? x : y; } inline Index assumeleft_minIndex(const Val *a, Index x, Index y) const { return comp(a[y], a[x]) ? y : x; } inline Val minVal(Val x, Val y) const { return comp(y, x) ? y : x; } void buildSparseTable(const Val *a) { Index *b = sparseTable; if (stHeight) for (Index i = 0; i < blocks; i ++) b[i] = i * BlockSize + blockTypes[i][0][BlockSize - 1]; for (Index t = 1; t * 2 < blocks; t *= 2) { std::memcpy(b + blocks, b, blocks * sizeof(Index)); b += blocks; for (Index i = 0; i < blocks - t; ++ i) b[i] = assumeleft_minIndex(a, b[i], b[i + t]); } } void buildInnerBlockTable(const Val *a, Index n) { for (Index i = 0; i < blocks; i ++) { BlockTypeRef table = blockTypes[i]; if (table[0][0] != -1) continue; const Val *p = getBlock(a, n, i); for (InBlockIndex left = 0; left < BlockSize; left ++) { Val minV = p[left]; InBlockIndex minI = left; for (InBlockIndex right = left; right < BlockSize; right ++) { if (comp(p[right], minV)) { minV = p[right]; minI = right; } table[left][right] = minI; } } } } //端っこのブロック用に関数内staticなテンポラリ配列を返す const Val *getBlock(const Val *a, Index n, Index i) { Index offset = i * BlockSize; if (offset + BlockSize <= n) return a + offset; else { static Val tmp_a[BlockSize]; std::copy(a + offset, a + n, tmp_a); Val maxVal = Val(); for (Index j = i; j < n; j ++) //iでなくoffsetでは?(動作には問題ないし計算量もほとんど変わらないけれど…)(バグるのが嫌なので(今まで動いていたので)直すのは後にする) if (comp(maxVal, a[j])) maxVal = a[j]; std::fill(tmp_a + (n - offset), tmp_a + BlockSize, maxVal); return tmp_a; } } void calcBlockTypes(const Val *a, Index n) { Val tmp_rp[BlockSize + 1]; for (Index i = 0; i < blocks; i ++) blockTypes[i] = calcBlockType(getBlock(a, n, i), tmp_rp); } BlockTypeRef calcBlockType(const Val *a, Val *rp) { int q = BlockSize, N = 0; for (int i = 0; i < BlockSize; i ++) { while (q + i - BlockSize > 0 && comp(a[i], rp[q + i - BlockSize])) { N += ballotNumbers[BlockSize - i - 1][q]; q --; } rp[q + i + 1 - BlockSize] = a[i]; } return innerBlockTable[N]; } void calcBallotNumbers() { for (int p = 0; p <= BlockSize; p ++) { for (int q = 0; q <= BlockSize; q ++) { if (p == 0 && q == 0) ballotNumbers[p][q] = 1; else if (p <= q) ballotNumbers[p][q] = (q ? ballotNumbers[p][q - 1] : 0) + (p ? ballotNumbers[p - 1][q] : 0); else ballotNumbers[p][q] = 0; } } } void buildInnerBlockTable() { int numberOfTrees = ballotNumbers[BlockSize][BlockSize]; innerBlockTable = new InBlockIndex[numberOfTrees][BlockSize][BlockSize]; for (int i = 0; i < numberOfTrees; i ++) innerBlockTable[i][0][0] = -1; } }; class SuffixArray { public: typedef char Alpha; typedef int Index; void build(const Alpha *str, Index n, int AlphaSize); void build(const Alpha *str, Index n); void buildAll(const Alpha *str, Index n); inline Index getKThSuffix(Index k) const { return suffixArray[k]; } inline Index length() const { return static_cast(suffixArray.size() - 1); } std::vector suffixArray; template void sa_is(const AlphaT *str, Index n, int AlphaSize, Index *sa, std::vector &bucketOffsets); template void inducedSort(const AlphaT *str, Index n, int AlphaSize, const std::vector &types, Index *sa, std::vector &bucketOffsets); template void countAlphabets(const AlphaT *str, Index n, int AlphaSize, std::vector &bucketOffsets, bool b = false); template void getBucketOffsets(const AlphaT *str, Index n, bool dir, int AlphaSize, std::vector &bucketOffsets); void buildInverseSuffixArray(); std::vector inverseSuffixArray; void computeLCPArray(const Alpha *str); std::vector lcpArray; typedef DirectRMQ LCPArrayRMQ; LCPArrayRMQ lcpArrayRMQ; void preprocessLCPArrayRMQ() { lcpArrayRMQ.build(&lcpArray[0], length() + 1); } Index computeLCP(Index i, Index j) const; }; void SuffixArray::build(const Alpha *str, Index n, int AlphaSize) { suffixArray.resize(n + 1); if (n == 0) suffixArray[0] = 0; else { //I = sizeof(Index) * CHAR_BITS として //suffixArray + bucketOffsets + types + 関数ローカル変数 //= n*I + max(AlphaSize, n/2)*I + 2*n + O(log n) bits //I = 4 * 32でAlphaSizeが十分小さいとすると: //(6+1/16) * n + O(log n) bytes std::vector bucketOffsets(std::max(AlphaSize, (n + 1) / 2) + 1); sa_is(str, n, AlphaSize, &suffixArray[0], bucketOffsets); } } void SuffixArray::build(const Alpha *str, Index n) { Alpha maxElem = *std::max_element(str, str + n); assert(maxElem + 0 < std::numeric_limits::max()); build(str, n, (int)(maxElem + 1)); } void SuffixArray::buildAll(const Alpha *str, Index n) { build(str, n); buildInverseSuffixArray(); computeLCPArray(str); preprocessLCPArrayRMQ(); } //strは[0,n)が有効で番兵は含まれない。saは[0,n]が有効 template void SuffixArray::sa_is(const AlphaT *str, Index n, int AlphaSize, Index *sa, std::vector &bucketOffsets) { std::vector types(n + 1); types[n - 1] = 0; types[n] = 1; for (Index i = n - 2; i >= 0; i --) types[i] = str[i] < str[i + 1] || (str[i] == str[i + 1] && types[i + 1]); countAlphabets(str, n, AlphaSize, bucketOffsets); getBucketOffsets(str, n, true, AlphaSize, bucketOffsets); std::fill(sa, sa + n + 1, -1); for (Index i = 1; i < n; i ++) if (types[i] && !types[i - 1]) sa[-- bucketOffsets[(int)str[i]]] = i; sa[0] = n; inducedSort(str, n, AlphaSize, types, sa, bucketOffsets); Index n1 = 0; for (Index i = 0; i <= n; i ++) { Index j = sa[i]; if (j > 0 && types[j] && !types[j - 1]) sa[n1 ++] = j; } //LMS substringsを番号付けする。sa[0..n1-1]にソートされている。 //メモリのためにsaの右半分をバッファに利用する。 //さらにそこでposの順序で整数ソートすることを同時に行う。 //ここでLMS substringが連続して現れないことやLMS substringの数がn/2以下であることを利用してなんとか1つの配列でやる Index *buffer = sa + n1; std::fill(buffer, sa + n + 1, -1); Index uniqueLMSCount = 0, prevPos = -1; assert(sa[0] == n); buffer[sa[0] / 2] = uniqueLMSCount ++; //'$' for (Index i = 1; i < n1; i ++) { Index pos = sa[i]; bool diff = false; if (prevPos == -1) diff = true; else for (Index j = pos, k = prevPos; ; j ++, k ++) { if (str[j] != str[k] || types[j] != types[k]) { diff = true; break; } else if (j != pos && ((types[j] && !types[j - 1]) || (types[k] && !types[k - 1]))) break; } if (diff) { uniqueLMSCount ++; prevPos = pos; } buffer[pos / 2] = uniqueLMSCount - 1; } for (Index i = n, j = n; i >= n1; i --) if (sa[i] >= 0) sa[j --] = sa[i]; Index *sa1 = sa, *s1 = sa + n + 1 - n1; if (uniqueLMSCount == n1) for (Index i = 0; i < n1; i ++) sa1[s1[i]] = i; else sa_is(s1, n1 - 1, uniqueLMSCount, sa1, bucketOffsets); countAlphabets(str, n, AlphaSize, bucketOffsets); getBucketOffsets(str, n, true, AlphaSize, bucketOffsets); for (Index i = 1, j = 0; i <= n; i ++) if (types[i] && !types[i - 1]) s1[j ++] = i; for (Index i = 0; i < n1; i ++) sa1[i] = s1[sa1[i]]; std::fill(sa + n1, sa + n + 1, -1); for (Index i = n1 - 1; i >= 1; i --) { Index j = sa[i]; sa[i] = -1; sa[-- bucketOffsets[(int)str[j]]] = j; } inducedSort(str, n, AlphaSize, types, sa, bucketOffsets); } template void SuffixArray::inducedSort(const AlphaT *str, Index n, int AlphaSize, const std::vector &types, Index *sa, std::vector &bucketOffsets) { getBucketOffsets(str, n, false, AlphaSize, bucketOffsets); for (Index i = 0; i < n; i ++) { Index j = sa[i] - 1; if (j >= 0 && !types[j]) sa[bucketOffsets[(int)str[j]] ++] = j; } getBucketOffsets(str, n, true, AlphaSize, bucketOffsets); for (Index i = n; i >= 1; i --) { Index j = sa[i] - 1; if (j >= 0 && types[j]) sa[-- bucketOffsets[(int)str[j]]] = j; } } template void SuffixArray::countAlphabets(const AlphaT *str, Index n, int AlphaSize, std::vector &bucketOffsets, bool b) { if (b || (int)bucketOffsets.size() / 2 >= AlphaSize) { std::vector::iterator alphabetCounts = b ? bucketOffsets.begin() : bucketOffsets.begin() + AlphaSize; std::fill(alphabetCounts, alphabetCounts + AlphaSize, 0); for (Index i = 0; i < n; i ++) alphabetCounts[(int)str[i]] ++; } } template void SuffixArray::getBucketOffsets(const AlphaT *str, Index n, bool dir, int AlphaSize, std::vector &bucketOffsets) { //AlphaSizeが大きい場合にはbucketOffset求めるたびにalphabetを数えてメモリ量を少なくし、 //AlphaSizeが小さい場合にはbucketOffsetをalphabetCountsと別の場所に置くことにする。 std::vector::iterator alphabetCounts; if ((int)bucketOffsets.size() / 2 < AlphaSize) { countAlphabets(str, n, AlphaSize, bucketOffsets, true); alphabetCounts = bucketOffsets.begin(); } else alphabetCounts = bucketOffsets.begin() + AlphaSize; Index cumsum = 1; //'$'の分 if (dir) { for (int i = 0; i < AlphaSize; i ++) { cumsum += alphabetCounts[i]; bucketOffsets[i] = cumsum; } } else { for (int i = 0; i < AlphaSize; i ++) { Index x = alphabetCounts[i]; bucketOffsets[i] = cumsum; cumsum += x; } } } void SuffixArray::buildInverseSuffixArray() { Index n = length(); inverseSuffixArray.resize(n + 1); for (Index i = 0; i <= n; i ++) inverseSuffixArray[suffixArray[i]] = i; } void SuffixArray::computeLCPArray(const Alpha *str) { int n = length(); lcpArray.resize(n + 2); Index h = 0; for (Index i = 0; i < n; i ++) { Index pos = inverseSuffixArray[i]; Index j = suffixArray[pos - 1]; Index hbound = std::min(n - j, n - i); for (Index k = 0; h < hbound && str[i + h] == str[j + h]; ++ h); lcpArray[pos - 1] = h; if (h > 0) -- h; } lcpArray[n] = lcpArray[n + 1] = 0; } SuffixArray::Index SuffixArray::computeLCP(Index i, Index j) const { Index n = length(); if (i == j) return n - i; Index x = inverseSuffixArray[i], y = inverseSuffixArray[j]; if (x > y) std::swap(x, y); return lcpArrayRMQ.queryVal(&lcpArray[0], x, y - 1); } int main() { int N; while (~scanf("%d", &N)) { string S; vector index(N); vector len(N); rep(i, N) { char buf[800001]; scanf("%s", buf); index[i] = (int)S.size(); len[i] = (int)strlen(buf); S += buf; S += '$'; } SuffixArray sa; sa.buildAll(S.c_str(), (int)S.size()); int M; long long x; long long d; scanf("%d%lld%lld", &M, &x, &d); ll anssum = 0; rer(k, 1, M) { int i = (int)(x / (N - 1)) + 1; int j = (int)(x % (N - 1)) + 1; if (i > j) swap(i, j); else j = j + 1; int ans = sa.computeLCP(index[i - 1], index[j - 1]); amin(ans, (int)len[i - 1]); amin(ans, (int)len[j - 1]); anssum += ans; x = (x + d) % ((ll)N * (N - 1)); } printf("%lld\n", anssum); } return 0; }