import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.Comparator; import java.util.InputMismatchException; import java.util.PriorityQueue; public class Q400UnrollUpTo3 { InputStream is; PrintWriter out; String INPUT = ""; void solve() { long[] s = new long[26]; for(int i = 0;i < 26;i++){ s[i] = nl(); if(s[i] < 0 || s[i] > 1_000_000_000_000_000_000L)throw new RuntimeException("s[i] out of range"); } char[] t = ns().toCharArray(); if(t.length < 1 || t.length > 1_000_000)throw new RuntimeException("t out of range"); for(char c : t){ if(!('a' <= c && c <= 'z'))throw new RuntimeException("t invalid char"); } int n = t.length; // 0? int[] freq = new int[26]; for(char c : t){ freq[c-'a']++; } for(int i = 0;i < 26;i++){ if(s[i] < freq[i]){ out.println(0); return; } } long ret = 1; double retd = 1; int[] lens = new int[n+1]; for(char ch = 'a';ch <= 'z';ch++){ int chi = ch-'a'; // chが連続している長さの列を作成 int len = 0; int p = 0; for(int i = 0;i < n;i++){ if(t[i] == ch){ len++; }else{ if(len > 0)lens[p++] = len; len = 0; } } if(len > 0)lens[p++] = len; if(p == 0)continue; if(p == 1 && lens[0] == 1){ // 1 // maximize y subject to y=S ret *= s[chi]; retd *= s[chi]; if(retd >= 3L<<61 || ret >= 1L<<62){ out.println("hel"); return; } continue; } if(p == 1 && lens[0] == 2){ // 2 // maximize y(y-1)/2 subject to y=S long y = s[chi]; double vd = (double)y*(y-1)/2; long v = c2(y); retd *= vd; ret *= v; if(retd >= 3L<<61 || ret >= 1L<<62){ out.println("hel"); return; } continue; } if(p == 2 && lens[0] == 1 && lens[1] == 1){ // 1 1 // maximize x*y subject to x+y=S long x = s[chi]/2; long y = (s[chi]+1)/2; ret *= x * y; retd *= (double)x * y; if(retd >= 3L<<61 || ret >= 1L<<62){ out.println("hel"); return; } continue; } if(p == 1 && lens[0] == 3){ // 3 // maximize y(y-1)(y-2)/6 subject to y=S long y = s[chi]; double vd = (double)y*(y-1)*(y-2)/6; long v = c3(y); retd *= vd; ret *= v; if(retd >= 3L<<61 || ret >= 1L<<62){ out.println("hel"); return; } continue; } if(p == 2 && (long)lens[0] * lens[1] == 2){ // 1 2 // maximize x*y(y-1)/2 subject to x+y = S // (S-y)y^2/2 // f'=2Sy-3y^2=0, y=2S/3 long vmax = -1; for(long y = Math.max(0, s[chi]*2/3-10);y <= s[chi]*2/3+10 && y <= s[chi];y++){ double vd = (double)(s[chi]-y)*y*(y-1)/2; long v = (s[chi]-y)*c2(y); if(vd >= 3L<<61 || v >= 1L<<62){ out.println("hel"); return; } vmax = Math.max(vmax, v); } assert vmax != -1; ret *= vmax; retd *= vmax; if(retd >= 3L<<61 || ret >= 1L<<62){ out.println("hel"); return; } continue; } if(p == 3 && lens[0] == 1 && lens[1] == 1 && lens[2] == 1){ // 1 1 1 // maximize x*y*z subject to x+y+z = S long x = s[chi]/3; long y = (s[chi]+1)/3; long z = (s[chi]+2)/3; ret *= x*y*z; retd *= (double)x*y*z; if(retd >= 3L<<61 || ret >= 1L<<62){ out.println("hel"); return; } continue; } // 最低限必要な数 for(int i = 0;i < p;i++){ s[chi] -= lens[i]; } if(s[chi] < 0){ // impossible out.println(0); return; } // {v, d} // (v+d+1)/(d+1)の降順 PriorityQueue pq = new PriorityQueue<>(10000, new Comparator(){ public int compare(int[] a, int[] b){ // (v1+d1)/d1 >= (v2+d2)/d2 return -Long.compare((long)a[0]*(b[1]+1), (long)b[0]*(a[1]+1)); } }); for(int i = 0;i < p;i++){ pq.add(new int[]{lens[i], 0}); } double lretd = retd; while(!pq.isEmpty() && s[chi] > 0){ int[] cur = pq.poll(); cur[1]++; long g = gcd(cur[0]+cur[1], cur[1]); lretd = lretd * (cur[0] + cur[1]) / cur[1]; ret = ret / (cur[1]/g) * ((cur[0]+cur[1])/g); if(lretd >= 3L<<61 || ret >= 1L<<62){ out.println("hel"); return; } pq.add(cur); s[chi]--; } } out.println(ret); } // C(n,3) public static long c3(long n) { long a = n, b = n-1, c = n-2; if(a % 2 == 0){ a /= 2; }else{ b /= 2; } if(a % 3 == 0){ a /= 3; }else if(b % 3 == 0){ b /= 3; }else{ c /= 3; } return a*b*c; } // C(n,2) public static long c2(long n) { long a = n, b = n-1; if(a % 2 == 0){ a /= 2; }else{ b /= 2; } return a*b; } public static long gcd(long a, long b) { while (b > 0) { long c = a; a = b; b = c % b; } return a; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new Q400UnrollUpTo3().run(); } private byte[] inbuf = new byte[1024]; private int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }