Problem Description

Paper quality and quantity have long been used to measure a research's scientific productivity and scientific impact. Citation, which is the total times a paper has been cited, is a common means to judge importance of a paper. However, with all these factors varying, a collegiate committee has problems when judging which research is doing better. For this reason, H-index is proposed and now widely used to combine the above factors and give accurate judgement. H-index is defined as:

A scientist has index h if h of [his] Np papers have at least h citations each, and the other(Np-h) papers have at most h citations each.

In other words, a scholar with an index of h has published h papers each of which has been cited by others at least h times. Note that H-index is always an integer. It's said that achiveing H-index of 18 means one is fully quality to be a professor, and H-index of 45 or higher could mean membership in the United States Academy of Sciences.

You are to calculate the H-index for all the researchers in the list, base on the given information.

Input

There are multiple scenarios in the input, terminated by a single zero(0).

Each of the scenarios begin with an integer N(1<=N<=100), means that there are N papers. N lines follow, each contain a string(not exceeding 20 characters long), representing the author of the corresponding paper, without white spaces in-between. Though it would be common for one paper written by several authors, there would be exactly one author of each of these papers. Finally, there are N lines of strings, containing '0's and '1's. If the j-th character in the i-th line is '1', it means the i-th paper cites the j-th paper. A paper could never cite itself.

Output

For each scenario, output as many lines as the number of authors given. Each line contains the author's name and his H-index. The list should be sorted first by H-index in descending order, than by name in alphabetic order(Actually, ASCII order. So 'B' is prior to 'a').

Output a blank line after each scenario.

Sample Input

4PeterPeterBobBob00001000110001000

Sample Output

Peter 2Bob 0

//小明的H-index表示小明发表的论文中至少有Ｈ篇论文，这Ｈ篇论文每篇至少引用Ｈ次 #include
      
       #include
       
        #include
        
         #include
         
          #include
          
           using namespace std;struct input{	string s;	int b;}a[110];struct output{	string s;	int b;}c[110];bool cmp(input x,input y){	if(x.s==y.s) return x.b>y.b;	else return x.s
           
            y.b;}int main(){ //freopen("a.txt","r",stdin); int n; while(cin>>n&&n) { int k,i,len,j; for(i=0;i
            
             >a[i].s; c[i].b=a[i].b=0; } for(i=0;i
             
              0) { if(m[len-1]-'0'==1&&i!=len-1) a[len-1].b++; //计算每篇论文被引用的数量 len--; } } sort(a,a+n,cmp); for(k=0,i=0;i
              
               c[k].b) c[k].b++; //计算Ｈ-index(注意a[i].b是按从大到小排序的) c[k].s=a[i].s; k++; } sort(c,c+k,cm); for(i=0;i
              
             
            
           
          
         
        
       
      

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