#!/usr/local/bin/node
function twoval(use,e){
    arr=[];
    check=[];
    val=[];
    for(twovali of use){
        for(twovalj of use){
            for(twovalk of e){
                    arr.push(twovali+twovalk+twovalj);
                    check.push(twovalk);
                    val.push(eval(twovali+twovalk+twovalj))
                
            }
        }
    }
    return arr;
}
/*----------------------*/
function maxcreate(maxuse,n){
		return (maxuse==1) ?
		 (n%2===0) ?
			 Math.pow(2,n/2) :
			 Math.pow(2,(n-3)/2)*3:
			Math.pow(maxuse,n)
		}
/*----------------------*/		
function numpos(str){
  function isNumber(x){ 
    if( typeof(x) != 'number' && typeof(x) != 'string' )
        return false;
    else 
        return (x == parseFloat(x) && isFinite(x));
  }
numposarr=[]
  numposarri=0
  while(numposarri<=str.length){
  if(isNumber(str.charAt(numposarri))){
    numposa=i;
    while(isNumber(str.charAt(numposarri))){
      numposarri++;
      }
    numposarr.push([numposa,numposarri-1]);
    }
    numposarri++;
  }
  return numposarr;
}
/*----------------------*/
function numpos(str){
  function isNumber(x){ 
    if( typeof(x) != 'number' && typeof(x) != 'string' )
        return false;
    else 
        return (x == parseFloat(x) && isFinite(x));
  }
numposarr=[]
  numposi=0
  while(numposi<=str.length){
  if(isNumber(str.charAt(numposi))){
    numposa=numposi
    while(isNumber(str.charAt(numposi))){
      numposi++
      }
    numposarr.push([numposa,numposi-1])
    }
    numposi++
  }
  return numposarr
}
/*----------------------*/
function change(a,b,start,end){
	return a.slice(0,start)+b+a.slice(end+1,a.length)
}
/*----------------------*/
function In(arr,x){
  return arr.indexOf(x)!=-1
}
/*----------------------*/
function bracketdelete(mathtext){
    function change(a,b,n){
        return a.slice(0, n-1)+b+a.slice(n, a.length);
    }
    
    function mojime(mathtext3,l){
        return mathtext3.slice(l-1,l);
    }
    function hantaibracket(mathtext2,m){
        var pos=m;
        var leftbracket=0;
        var rightbracket=0;
        while(leftbracket!=rightbracket||pos==m){
            if(mojime(mathtext2,pos)=="("){
                leftbracket+=1;
            }
            if(mojime(mathtext2,pos)==")"){
                rightbracket+=1;
            }
            pos++;
        }
        return pos-1;
    }
    var Flag=1;
    while(Flag==1){
        Flag=0;
        for(var i=1;i<=mathtext.length;i++){
            if(mojime(mathtext,i)=="("){
                hantai=hantaibracket(mathtext,i);
                if(mojime(mathtext,hantai+1)!="×" && mojime(mathtext,hantai+1)!="/" && mojime(mathtext,hantai+1)!="*" && mojime(mathtext,hantai+1)!="÷"){
                    if((mojime(mathtext,i-1)==" "||mojime(mathtext,i-1)=="+")){
                        mathtext=change(mathtext,"@",i);
                        mathtext=change(mathtext,"@",hantai);
                        Flag=1;
                    }
                    if((mojime(mathtext,i-1)=="-")){
                        for(var j=i+1;j<=hantai-1;j++){
                            if(mojime(mathtext,j)=="+"){
                                mathtext=change(mathtext,"-",j);
                                continue;
                            }else if(mojime(mathtext,j)=="-"){
                                mathtext=change(mathtext,"+",j);
                                continue;
                            }else if(mojime(mathtext,j)=="("){
                                j=hantaibracket(mathtext,j);
                            }
                        }
                            
                        
                        mathtext=change(mathtext,"@",i);
                        mathtext=change(mathtext,"@",hantai);
                        Flag=1;
                    }                
                }
    
                
            }
        }
        mathtext=mathtext.replace( /@/g ,"");
    }
    return mathtext;
}
/*----------------------*/
function index(arr,n,key){
  for(indexi of arr){
    if(indexi[n]==key){
      return indexi
    }
  }
  return -1;
}
/*----------------------*/
function indexpos(arr,n,key){
  for(posi in arr){
    if(arr[posi][n]==key){
      return posi
    }
  }
  return -1;
}
/*----------------------*/
function numpos2(str){
  pos2arr=[]
  pos2arr2=[]
  pos2pos=numpos(str)
  for (numpos2_i=0;numpos2_i<pos2pos.length;numpos2_i++){
    for (numpos2_j=0;numpos2_j<=numpos2_i;numpos2_j++){
      E=eval(change(str,"100",pos2pos[numpos2_i][0],pos2pos[numpos2_i][1]))
      if(!In(pos2arr2,E)){
        pos2arr.push(pos2pos[numpos2_i])
        pos2arr2.push(E)
      }
    }
  }
  return pos2arr
}
/*----------------------*/
function add(str,use,e){
  addarr=[]
  for(add_i of numpos2(str)){
    for(add_j of twoval(use,e)){
      addarr.push(change(str,"("+add_j+")",add_i[0],add_i[1]))
    }
  }
  return addarr
}
/*----------------------*/
function EvalDelete(arr){
  Ev=[]
  return arr.filter(function (element, index, array){
    if(In(Ev,eval(element))){
      return false
    }else{
      Ev.push(eval(element))
      return true
    }
  });
}
/*----------------------*/
function find(use, target, e) {
  
  function Delete(Delete_k,Delete_n,Delete_X){
    Delete_Eval=eval(Delete_X)
    Delete_maxadd=maxcreate(Math.max.apply(null, use),Delete_n-Delete_k)
    haijo=[
    Math.max(Math.abs(Delete_Eval)+Delete_maxadd , Math.abs(Delete_Eval*Delete_maxadd)) < Math.abs(target),
    Math.abs(Delete_Eval)-Delete_maxadd > Math.abs(target),
    ];
    if(In(haijo,true)){
      return 0;
    }
    for(Ei=1;Ei<Delete_k;Ei++){
      for(Ej of Storage[Ei]){
        if(Ej==Delete_Eval){
          return 0
        }      
      }
    }
    return 1
    
  }
  function f(k, n, X) {
    if(count%10000===0&&count!=0){
      console.log(I+"周目の"+count+"回目まで探索しました")
    }
    count++
    Eval=eval(X)
    if(Eval!==0&&!In(Storage[k],Eval)){
      Storage[k].push(Eval)
    }
    
    if (k == n) {
      if (Eval == target) {
        console.log(I+"周目で発見しました")
        console.log(bracketdelete(target+" = "+X));
        return 1;
      } else {
        return 0;
      }
    } else {
      for(var i of EvalDelete(add(X,use,e))){
          if(Delete(k + 1, n,i)===0){
            continue;
          }
          if(f(k + 1, n,i)==1){
            return 1
          }
      }
      return 0;
    }
  }
  count=0
  Storage=[[]]
  for(I=1;I<=10;I++){
    count=0
    if(Storage[I]==undefined)
      Storage[I]=[]
    if(f(0, I, '0')==1){
      return
    }
    console.log(I+"周目の探索が終了しました")
    //console.log(I,count)
  }
}
Target=12
Use=[11,13]
E=['+', '-', '*']
console.log(Target+"を"+Use+"と"+E+"に分解します\n")
find(Use, Target, E);