#include #include #include #define unlikely(x) __builtin_expect(!!(x), 0) struct char_reader { FILE *f; char *buf, *p1, *p2; int size; char_reader(FILE *fin, int bufsize = 1 << 16) { f = fin; size = bufsize; p1 = p2 = 0; buf = new char[size]; } ~char_reader() { delete[] buf; } inline int operator()() { return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, size, f), p1 == p2) ? EOF : *p1++; } }; struct char_writer { FILE *f; char *buf, *p, *end; int size; char_writer(FILE *fout, int bufsize = 1 << 16) { f = fout; size = bufsize; buf = new char[size]; p = buf; end = buf + bufsize; } ~char_writer() { fwrite(buf, p - buf, 1, f); delete[] buf; } inline char operator()(char ch) { if (unlikely(end == p)) { fwrite(buf, end - buf, 1, f); p = buf; } return *p++ = ch; } }; char_reader gch(stdin); char_writer wch(stdout); template inline int read(T &t) { bool f = false; int ch; while (ch = gch(), !((ch >= '0' && ch <= '9') || ch == '-')) { if (ch == EOF) return 0; } t = 0; if (ch == '-') f = true, ch = gch(); t = ch ^ 48; while (ch = gch(), ch >= '0' && ch <= '9') t = (t << 3) + (t << 1) + (ch ^ 48); if (f) t = -t; return 1; } inline int read(char &c) { c = 0; int ch; while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) { if (ch == EOF) return 0; } c = ch; return 1; } inline int read(char *s) { int ch; while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) { if (ch == EOF) return 0; } *s++ = ch; while (ch = gch(), !(ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t') && ch != EOF) *s++ = ch; *s++ = 0; return 1; } inline int read(const char *s) { return read((char *)s); } inline int readline(char *s) { int ch; while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) { if (ch == EOF) return 0; } *s++ = ch; while (ch = gch(), !(ch == '\n' || ch == '\r') && ch != EOF) *s++ = ch; *s++ = 0; return 1; } inline int readline(const char *s) { return readline((char *)s); } template inline void write(T t) { int stk[20], cnt = 0; if (t == 0) { wch('0'); return; } if (t < 0) { wch('-'); t = -t; } while (t > 0) { stk[cnt++] = t % 10; t /= 10; } while (cnt) wch(stk[--cnt] + '0'); } inline void write(char t) { wch(t); } inline void write(char *s) { while (*s) wch(*s++); } inline void write(const char *s) { write((char *)s); } #if __cplusplus >= 201103L template inline int read(T &t, Args &...args) { return read(t) + read(args...); } template inline void write(T t, Args... args) { write(t); write(args...); } #else template inline int read(A_t &a, B_t &b) { return read(a) + read(b); } template inline int read(A_t &a, B_t &b, C_t &c) { return read(a) + read(b) + read(c); } template inline int read(A_t &a, B_t &b, C_t &c, D_t &d) { return read(a) + read(b) + read(c) + read(d); } template inline void write(A_t a, B_t b) { write(a); write(b); } template inline void write(A_t a, B_t b, C_t c) { write(a); write(b); write(c); } template inline void write(A_t a, B_t b, C_t c, D_t d) { write(a); write(b); write(c); write(d); } #endif using namespace std; typedef long long LL; const int kMaxN = 3e5 + 10; const LL kInf = 1e18 + 10; int n; char s[kMaxN]; int sa[kMaxN * 2], rk[kMaxN * 2], height[kMaxN]; LL a[kMaxN]; namespace __SA_IS { int str[kMaxN * 2], sa[kMaxN * 2], typ[kMaxN * 2], c[kMaxN], p[kMaxN * 2], sbuc[kMaxN], lbuc[kMaxN], name[kMaxN]; inline int islms(int *typ, int i) { return !typ[i] && (i == 1 || typ[i - 1]); } int cmp(int *s, int *typ, int p, int q) { do { if (s[p] != s[q]) return 1; p++; q++; } while (!islms(typ, p) && !islms(typ, q)); return (!islms(typ, p) || !islms(typ, q) || s[p] != s[q]); } void isort(int *s, int *sa, int *typ, int *c, int n, int m) { int i; for (lbuc[0] = sbuc[0] = c[0], i = 1; i <= m; i++) { lbuc[i] = c[i - 1] + 1; sbuc[i] = c[i]; } for (i = 1; i <= n; i++) if (sa[i] > 1 && typ[sa[i] - 1]) sa[lbuc[s[sa[i] - 1]]++] = sa[i] - 1; for (i = n; i >= 1; i--) if (sa[i] > 1 && !typ[sa[i] - 1]) sa[sbuc[s[sa[i] - 1]]--] = sa[i] - 1; } void build_sa(int *s, int *sa, int *typ, int *c, int *p, int n, int m) { int i; for (i = 0; i <= m; i++) c[i] = 0; for (i = 1; i <= n; i++) c[s[i]]++; for (i = 1; i <= m; i++) c[i] += c[i - 1]; typ[n] = 0; for (i = n - 1; i >= 1; i--) if (s[i] < s[i + 1]) typ[i] = 0; else if (s[i] > s[i + 1]) typ[i] = 1; else typ[i] = typ[i + 1]; int cnt = 0; for (i = 1; i <= n; i++) if (!typ[i] && (i == 1 || typ[i - 1])) p[++cnt] = i; for (i = 1; i <= n; i++) sa[i] = 0; for (i = 0; i <= m; i++) sbuc[i] = c[i]; for (i = 1; i <= cnt; i++) sa[sbuc[s[p[i]]]--] = p[i]; isort(s, sa, typ, c, n, m); int last = 0, t = -1, x; for (i = 1; i <= n; i++) { x = sa[i]; if (!typ[x] && (x == 1 || typ[x - 1])) { if (!last || cmp(s, typ, x, last)) name[x] = ++t; else name[x] = t; last = x; } } for (i = 1; i <= cnt; i++) s[n + i] = name[p[i]]; if (t < cnt - 1) build_sa(s + n, sa + n, typ + n, c + m + 1, p + n, cnt, t); else for (i = 1; i <= cnt; i++) sa[n + s[n + i] + 1] = i; for (i = 0; i <= m; i++) sbuc[i] = c[i]; for (i = 1; i <= n; i++) sa[i] = 0; for (i = cnt; i >= 1; i--) sa[sbuc[s[p[sa[n + i]]]]--] = p[sa[n + i]]; isort(s, sa, typ, c, n, m); } } // namespace __SA_IS void SA_IS(char *s, int n, int *sa, int *rk) { using namespace __SA_IS; for (int i = 1; i <= n; i++) str[i] = s[i]; str[++n] = 0; build_sa(str, sa, typ, c, p, n, 256); n--; for (int i = 1; i <= n; i++) sa[i] = sa[i + 1]; for (int i = 1; i <= n; i++) rk[sa[i]] = i; } void computeHeight(char *s, int n, int *sa, int *rk, int *height) { int k = 0; for (int i = 1; i <= n; i++) { if (rk[i] == 1) { height[rk[i]] = 0; continue; } if (k > 0) { k--; } int j = sa[rk[i] - 1]; while (i + k <= n && j + k <= n && s[i + k] == s[j + k]) { k++; } height[rk[i]] = k; } } LL exact_method[kMaxN], exact_yammy[kMaxN]; struct H_Struct { int height_index, height_value; H_Struct() {} H_Struct(int __h_i, int __h_v) : height_index(__h_i), height_value(__h_v) {} }; bool operator<(const H_Struct &A, const H_Struct &B) { return A.height_value > B.height_value; } H_Struct merge_pair[kMaxN]; int fa[kMaxN], min_a[kMaxN], max_a[kMaxN], subtree_size[kMaxN]; LL subtree_max_yammy[kMaxN]; inline int ff(int u) { int v = u, x; while (u != fa[u]) u = fa[u]; while (v != u) { x = fa[v]; fa[v] = u; v = x; } return u; } int main() { #ifdef local freopen("pro.in", "r", stdin); #endif read(n); read(s + 1); for (int i = 1; i <= n; i++) read(a[i]); SA_IS(s, n, sa, rk); computeHeight(s, n, sa, rk, height); for (int i = 2; i <= n; i++) merge_pair[i - 1] = H_Struct(i, height[i]); sort(merge_pair + 1, merge_pair + 1 + n - 1); for (int i = 1; i <= n; i++) { fa[i] = i; max_a[i] = min_a[i] = a[i]; subtree_size[i] = 1; subtree_max_yammy[i] = -kInf; exact_yammy[i] = -kInf; } for (int i = 1; i <= n - 1; i++) { int x = sa[merge_pair[i].height_index]; int y = sa[merge_pair[i].height_index - 1]; int ht = merge_pair[i].height_value; // printf("%d and %d\n", x, y); x = ff(x); y = ff(y); fa[y] = x; exact_method[ht] += (LL)subtree_size[x] * (LL)subtree_size[y]; // 可以归纳证明当多个height相同时,这个递推方式也是正确的 subtree_size[x] += subtree_size[y]; subtree_max_yammy[x] = max(subtree_max_yammy[x], subtree_max_yammy[y]); // printf("smy %d %lld\n", x, subtree_max_yammy[x]); subtree_max_yammy[x] = max(subtree_max_yammy[x], max(min_a[x] * (LL)min_a[y], max_a[x] * (LL)max_a[y])); // printf("smy %d %lld\n", x, subtree_max_yammy[x]); subtree_max_yammy[x] = max(subtree_max_yammy[x], max(max_a[x] * (LL)min_a[y], min_a[x] * (LL)max_a[y])); // printf("smy %d %lld\n", x, subtree_max_yammy[x]); min_a[x] = min(min_a[x], min_a[y]); max_a[x] = max(max_a[x], max_a[y]); // printf("mm %d %d\n", x, max_a[x]); // printf("mi %d %d\n", x, min_a[x]); exact_yammy[ht] = max(exact_yammy[ht], subtree_max_yammy[x]); // 这里很显然 } for (int i = n - 2; i >= 0; i--) { exact_method[i] += exact_method[i + 1]; exact_yammy[i] = max(exact_yammy[i], exact_yammy[i + 1]); } for (int i = 0; i <= n - 1; i++) printf("%lld %lld\n", exact_method[i], exact_method[i] != 0 ? exact_yammy[i] : 0); return 0; }