#!/bin/bash
gcc -O2 -x c - -o cal-mean <<EOF
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
typedef union {
	uint64_t i;
	double p;
}data_t;
data_t * data;

double cal_mean(int *n, int sub_pos, int a_cnt, const double *p, const int *seq)
{
	int i, pos = 0;
	double f1 = 1.0, f2 = 1.0;

	if(a_cnt == 0) {
		n[sub_pos]++;
		return 0.0;
	}
	for(i=0;i<11;i++)
		pos += n[i]*seq[i];
	if(data[pos].i) {
		n[sub_pos]++;
		return data[pos].p;
	}
	for(i=0;i<11;i++) {
		if(n[i]) {
			n[i]--;
			f1 += cal_mean(n,i,a_cnt-1,p,seq) * p[i];
		} else {
			f2 -= p[i];
		}
	}
	f1 /= f2;
	data[pos].p = f1;
	n[sub_pos]++;
	return f1;
}

int main(int argc, char**argv)
{
	int i, n[11], seq[11];
	double mean, p[11];

	data = malloc(sizeof(data_t)*atoi(argv[1]));
	if(data == NULL) {
		return 1;
	}
	for(i=0;i<11;i++) {
		p[i] = (6-(i+1)/2)/36.0;
	}

	while(1) {
		if(11 != scanf("%d%d%d%d%d%d%d%d%d%d%d",
					&n[0],&n[1],&n[2],&n[3],&n[4],&n[5],
					&n[6],&n[7],&n[8],&n[9],&n[10]))
			break;
		for(i=0;i<11;i++)
			printf("%d ",n[i]);
		seq[0] = 1;
		for(i=1;i<11;i++)
			seq[i] = seq[i-1]*(n[i-1]+1);
		memset(data,0,sizeof(data_t)*seq[10]*(n[10]+1));
		mean = cal_mean(n,0,36,p,seq);
		printf("%.8lf\n", mean);
	}
	free(data);
	return 0;
}
EOF

racket <(cat <<EOF
#lang scheme
(define (list-all n pieces max-num)
 (if (= pieces 1)
  (if (> n max-num) '() (list (list n)))
  (apply append
   (map
    (lambda (a) (map (lambda (x) (cons a x)) (list-all (- n a) (- pieces 1) a)))
    (range 0 (+ (min n max-num) 1))))))
(define (pr lst) (if (null? lst) (newline) (begin (display (car lst)) (write-char #\space) (pr (cdr lst)))))
(for-each pr (list-all 36 11 36))
EOF
) >input.txt

./cal-mean $(awk '{x=1;for(i=1;i<=NF;i++)x*=$i+1;if(size<x)size=x}END{print size}' input.txt) <input.txt >output.txt
sort -k 12 -n output.txt | head -n 1