/////////////////////////////////////////////////////////
//
//  ~/Izumi_Chiharu/c/temp.cpp file
//  Last Updated: 2018-06-17 ...Maybe
//
//    I hope you adding this code to the setting file
//    alias g++='g++ -std=c++1y -DDEBUG_LOCAL'
//
//  My sweet heart Chiharu Izumi
//
/////////////////////////////////////////////////////////

#include <bits/stdc++.h>

using namespace std;

void print_Qbey(){cout<<
"           H                                           M#5J~d              "  <<endl<<
"         Hm.?WMM                                   MMB^ .Z  d              "  <<endl<<
"         MZS.` ?7WMM                             M#=`` (!`` d              "  <<endl<<
"         HP?X,```  ?TMM                       MMY! ` .d: `` d              "  <<endl<<
"         Hb;<U,`````` (TMM                 HM ^ ``` .V>_` `.W              "  <<endl<<
"           ;><?n. `` ````?WHHMMHHHMMMMMM MMY```` ` (3<< `` .M              "  <<endl<<
"         HN<>>>?W,`` `` ` (77!~`  ```~!?7'``` `` .d>>><``  .M              "  <<endl<<
"          M2<>>>>?n.`` `` `` `` ``` `` ```` `` `.X>1++< `` (H              "  <<endl<<
"          MK<>>>>+?S.``` `` ```` ``` ``` `` `` .Z``` ?4-.` jM              "  <<endl<<
"           N2><+d=(Y^ `` `` ` ` ` ` `` `` `` `` T~.`````?=(dM              "  <<endl<<
"           MR;JY~`~``` `` `` ``` ``` `` `` `` ``` u, `` `` 7M              "  <<endl<<
"            NV!_`` `` `` ```` ``` `` `` `` ``` ``` C& ` ```` TMM           "  <<endl<<
"           MY.(-`` ` `` ``  `` ` `` `` `` `` ``  `` (n ` ` ``` 7M          "  <<endl<<
"         HMD-(D`` ``` `` ``` `` `` `` `` `` ` ``` ```(n ` `` `` (WM        "  <<endl<<
"         M _(d```` `` ``` ``` ``` `` `` `` ``` ``` `` .b.`` `` ```?MH      "  <<endl<<
"        MM!_(%` `` `` `` ` ` `` `` `` ``` `` `` ` `` ` (l`` ``````` TMH    "  <<endl<<
"       H#>__d:`` .JXVS, ``` `` ` `` `` `.JXWH&.``` ```` O; `` ` ` `` -WM   "  <<endl<<
"       M%.~(k ``.HXH[ dr ```` ``` `` `` dWWN- u. `` ``` ,M,``` ``` ``` ?MMM"  <<endl<<
"      MF_~~($`` .WXMMWX$ ` ``` `` ``` ` dXM HHK````` `` ,HN-``````````.-=jg"  <<endl<<
"MMMMHMY.~~~(R ``` 799Y!```` ``` `` `` `` ?UUUY!`` ````` (M N, `` ```.Z3J=``"  <<endl<<
"gaJJdD.~~::_X|`````````````` `````` `` ` ``` ````` ``` .H  MN,``` .Yiv! ```"  <<endl<<
"   MD_:~:~:~(T.`````````` ``` ` ` ````` ``` ``` ``````.M     N, .Ziv!`` ._~"  <<endl<<
" MM'_:::::::~(N+.`````````` .`.(.` .` ``` ```` ```` .dM       NZ1v! .-_~~``"  <<endl<<
" #:(::::::::~(HMNa..  ``````_?!`?7! `` ````  ...-(+7WMM     HM3(b _:<``..`."  <<endl<<
"=_;::::::::<(H    MMHaJ--_--........-.__~~~~(&v7<~``` ?MM   M>gM9h,_......."  <<endl<<
";;;;;;;:;::(drWM          HHmgggg&gzOtOzz<<~~~~~_`` ``` ?MMMH+ggM Mm-......"  <<endl<<
"e<>>;>>;;><dMMJM                  Nc_~~~~~~~~~~_ ``  ` `` 7H&-...?THNe-_._("  <<endl<<
",4m+>>>>>>j MM(W                   N-~~~~~~~~:_`` ``` ` ``  ?7UHHqqHWHMm+__"  <<endl<<
"vX+vT4k&&dMMD!+M                   MR_~~~~~:_````` ```` ````````` ````  ?We"  <<endl<<
"???zTwiJ-(((JdM                    MK_~~~~:_``` ` ` ` `` ` ` ` ``` ```````?"  <<endl<<
"1uukgHM                            MH_~~~_``` `` ``` `` `` `` ` `` ` `  ```"  <<endl<<
"CugM                                N;~~:_ ` `` `` ``` `` ````` ``` ``` ` `"  <<endl<<
"H                                   M[~~~_4, `   ` `` `` ``  ``` `` `` ``` "  <<endl<<
"                                    Hb~~~~~?n  (: `` `` `` `` ` ` `` `` ```"  <<endl<<
"                                    Hb~~~~~~(4,J_ `` ```  ```` ``` `` `` ` "  <<endl<<
"                                     N-~~~~~~(MM_` `` ` (}  `` `` `` `` ```"  <<endl<<
"                                     Mr_~~~~~(HH: `` `` j!`` `` `` `` `` ``"  <<endl<<
"                                     Mb~~~~~~(WH:`` `` .Z `` `` `` ``` `` `"  <<endl<<
"                                      N:~~~~~(WM{ `` ` .H+.. `` `  .``` `` "  <<endl;}

#define fi first
#define se second
#define mp make_pair
#define pb push_back

//#define int long long

#define _overload3(_1,_2,_3,name,...) name
#define _REP(i,n) REAP(i,0,n)
#define REAP(i,a,b) for(int i=int(a);i<int(b);++i)
#define REP(...) _overload3(__VA_ARGS__,REAP,_REP,)(__VA_ARGS__)

#define _REPR(i,n) REAPR(i,n,0)
#define REAPR(i,a,b) for(int i=int(a-1);i>=int(b);--i)
#define REPR(...) _overload3(__VA_ARGS__,REAPR,_REPR,)(__VA_ARGS__)

#define ALL(a) a.begin(),a.end()
#define rALL(a) a.rbegin(),a.rend()

#define coutALL(a) {int loop_coutALL=0;for(auto e:a) cout<<(loop_coutALL++?" ":"")<<e; cout<<endl;}
#define coutYN(a) cout<<(a?"Yes":"No")<<endl;
#define coutyn(a) cout<<(a?"yes":"no")<<endl;

#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)

const int INF=1145141919;
const int MOD=(int)1e9+7;
const double EPS=1e-12;
const int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
//const int dx[]={-1,-1,-1,0,1,1,1,0},dy[]={-1,0,1,1,1,0,-1,-1};

using vi=vector<int>;
using vvi=vector<vi>;
using vs=vector<string>;

typedef pair<int,int> pii;
typedef pair<int,string> pis;
typedef pair<string,int> psi;
typedef pair<string,string> pss;

typedef long long ll;

template<class T> ll upper(T n,T m){return (n+m-1)/m;};
template<class T> ll rounding(T n){return (long double)n+0.5;};

inline int qp(int a,ll b){int ans=1;do{if(b&1)ans=1ll*ans*a;a=1ll*a*a;}while(b>>=1);return ans;}
inline int qp(int a,ll b,int mo){int ans=1;do{if(b&1)ans=1ll*ans*a%mo;a=1ll*a*a%mo;}while(b>>=1);return ans;}

struct Arithmetic{Arithmetic(){cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);}};

//#define DEBUG_LOCAL

#ifdef DEBUG_LOCAL
template<typename T> void deb(T a){cerr<<"deb: "<<a<<"ですねぇ！"<<endl;}
#define debl {cerr<<"debug: "<<__LINE__<<"行目だよーんおほほ"<<endl;}
void what_cr(){cout<<__GCC_ATOMIC_CHAR16_T_LOCK_FREE<<" ←なんだろーこの数字？"<<endl;}
void t_t(){cout
    <<endl
    <<"------------------------"<<endl
    <<"| Presented by         |"<<" Compiled "<<__FILE__<<endl
    <<"| "<<__DATE__<<" "<<__TIME__<<" |"<<endl
    <<"|        Chiharu Izumi |"<<"      to get the AC :)"<<endl
    <<"------------------------"<<endl;
}
#else
template<typename T>void deb(T a){}
#define debl ;
void what_cr(){}void t_t(){}
#endif

int ans,flag[10];
vi ori(9);

void dfs(int now,vi &num){

  if(now==9){

    int ans1=num[0]+num[1]*10+num[2]+num[3]*100+num[4]*10+num[5];
    int ans2=num[6]*100+num[7]*10+num[8];

    ans+=(ans1==ans2);

    return;

  }

  if(num[now]){

    dfs(now+1,num);
    return;

  }

  REP(i,1,10){

    if(flag[i]) continue;

    flag[i]=1;
    num[now]=i;

    dfs(now+1,num);

    flag[i]=0;
    num[now]=0;

  }


}

signed main(){

  Arithmetic Exception;

  REP(i,9){

    cin>>ori[i];

    if(ori[i]==-1) ori[i]=0;
    else flag[ori[i]]=1;
  }

  dfs(0,ori);

  cout<<ans<<endl;

  return 0;

}


### Prompt

In cpp, your task is to solve the following problem:

Addition is easy to calculate by hand, but if some numbers are missing, is it easy to fill in the missing numbers? For example, in the following long division, if there is a condition that the numbers 1 to 9 appear only once, how many numbers will fit in the C and E squares? In this case, 8 is correct for C and 5 is correct for E. An operation that lacks some numbers in this way is called worm-eaten calculation.

<image>



The condition that the numbers 1 to 9 appear only once remains the same, and if more numbers are missing as shown below, is there only one way to fill in the correct numbers? In fact, it is not always decided in one way.

<image>



Create a program that outputs how many correct filling methods are available when the information of each cell from A to I is given in the form of worm-eaten calculation as shown in the above figure.



Input

The input is given in the following format.


A B C D E F G H I


One line is given the information of the numbers in the cells from A to I of the worm-eaten calculation. However, when the given value is -1, it means that the number in that square is missing. Values ​​other than -1 are any of the integers from 1 to 9 and there is no duplication between them.

Output

Outputs how many correct filling methods are available on one line.

Examples

Input

7 6 -1 1 -1 9 2 3 4


Output

1


Input

7 6 5 1 8 9 2 3 4


Output

0


Input

-1 -1 -1 -1 -1 -1 8 4 6


Output

12


Input

-1 -1 -1 -1 -1 -1 -1 -1 -1


Output

168

### Response

```cpp
/////////////////////////////////////////////////////////
//
//  ~/Izumi_Chiharu/c/temp.cpp file
//  Last Updated: 2018-06-17 ...Maybe
//
//    I hope you adding this code to the setting file
//    alias g++='g++ -std=c++1y -DDEBUG_LOCAL'
//
//  My sweet heart Chiharu Izumi
//
/////////////////////////////////////////////////////////

#include <bits/stdc++.h>

using namespace std;

void print_Qbey(){cout<<
"           H                                           M#5J~d              "  <<endl<<
"         Hm.?WMM                                   MMB^ .Z  d              "  <<endl<<
"         MZS.` ?7WMM                             M#=`` (!`` d              "  <<endl<<
"         HP?X,```  ?TMM                       MMY! ` .d: `` d              "  <<endl<<
"         Hb;<U,`````` (TMM                 HM ^ ``` .V>_` `.W              "  <<endl<<
"           ;><?n. `` ````?WHHMMHHHMMMMMM MMY```` ` (3<< `` .M              "  <<endl<<
"         HN<>>>?W,`` `` ` (77!~`  ```~!?7'``` `` .d>>><``  .M              "  <<endl<<
"          M2<>>>>?n.`` `` `` `` ``` `` ```` `` `.X>1++< `` (H              "  <<endl<<
"          MK<>>>>+?S.``` `` ```` ``` ``` `` `` .Z``` ?4-.` jM              "  <<endl<<
"           N2><+d=(Y^ `` `` ` ` ` ` `` `` `` `` T~.`````?=(dM              "  <<endl<<
"           MR;JY~`~``` `` `` ``` ``` `` `` `` ``` u, `` `` 7M              "  <<endl<<
"            NV!_`` `` `` ```` ``` `` `` `` ``` ``` C& ` ```` TMM           "  <<endl<<
"           MY.(-`` ` `` ``  `` ` `` `` `` `` ``  `` (n ` ` ``` 7M          "  <<endl<<
"         HMD-(D`` ``` `` ``` `` `` `` `` `` ` ``` ```(n ` `` `` (WM        "  <<endl<<
"         M _(d```` `` ``` ``` ``` `` `` `` ``` ``` `` .b.`` `` ```?MH      "  <<endl<<
"        MM!_(%` `` `` `` ` ` `` `` `` ``` `` `` ` `` ` (l`` ``````` TMH    "  <<endl<<
"       H#>__d:`` .JXVS, ``` `` ` `` `` `.JXWH&.``` ```` O; `` ` ` `` -WM   "  <<endl<<
"       M%.~(k ``.HXH[ dr ```` ``` `` `` dWWN- u. `` ``` ,M,``` ``` ``` ?MMM"  <<endl<<
"      MF_~~($`` .WXMMWX$ ` ``` `` ``` ` dXM HHK````` `` ,HN-``````````.-=jg"  <<endl<<
"MMMMHMY.~~~(R ``` 799Y!```` ``` `` `` `` ?UUUY!`` ````` (M N, `` ```.Z3J=``"  <<endl<<
"gaJJdD.~~::_X|`````````````` `````` `` ` ``` ````` ``` .H  MN,``` .Yiv! ```"  <<endl<<
"   MD_:~:~:~(T.`````````` ``` ` ` ````` ``` ``` ``````.M     N, .Ziv!`` ._~"  <<endl<<
" MM'_:::::::~(N+.`````````` .`.(.` .` ``` ```` ```` .dM       NZ1v! .-_~~``"  <<endl<<
" #:(::::::::~(HMNa..  ``````_?!`?7! `` ````  ...-(+7WMM     HM3(b _:<``..`."  <<endl<<
"=_;::::::::<(H    MMHaJ--_--........-.__~~~~(&v7<~``` ?MM   M>gM9h,_......."  <<endl<<
";;;;;;;:;::(drWM          HHmgggg&gzOtOzz<<~~~~~_`` ``` ?MMMH+ggM Mm-......"  <<endl<<
"e<>>;>>;;><dMMJM                  Nc_~~~~~~~~~~_ ``  ` `` 7H&-...?THNe-_._("  <<endl<<
",4m+>>>>>>j MM(W                   N-~~~~~~~~:_`` ``` ` ``  ?7UHHqqHWHMm+__"  <<endl<<
"vX+vT4k&&dMMD!+M                   MR_~~~~~:_````` ```` ````````` ````  ?We"  <<endl<<
"???zTwiJ-(((JdM                    MK_~~~~:_``` ` ` ` `` ` ` ` ``` ```````?"  <<endl<<
"1uukgHM                            MH_~~~_``` `` ``` `` `` `` ` `` ` `  ```"  <<endl<<
"CugM                                N;~~:_ ` `` `` ``` `` ````` ``` ``` ` `"  <<endl<<
"H                                   M[~~~_4, `   ` `` `` ``  ``` `` `` ``` "  <<endl<<
"                                    Hb~~~~~?n  (: `` `` `` `` ` ` `` `` ```"  <<endl<<
"                                    Hb~~~~~~(4,J_ `` ```  ```` ``` `` `` ` "  <<endl<<
"                                     N-~~~~~~(MM_` `` ` (}  `` `` `` `` ```"  <<endl<<
"                                     Mr_~~~~~(HH: `` `` j!`` `` `` `` `` ``"  <<endl<<
"                                     Mb~~~~~~(WH:`` `` .Z `` `` `` ``` `` `"  <<endl<<
"                                      N:~~~~~(WM{ `` ` .H+.. `` `  .``` `` "  <<endl;}

#define fi first
#define se second
#define mp make_pair
#define pb push_back

//#define int long long

#define _overload3(_1,_2,_3,name,...) name
#define _REP(i,n) REAP(i,0,n)
#define REAP(i,a,b) for(int i=int(a);i<int(b);++i)
#define REP(...) _overload3(__VA_ARGS__,REAP,_REP,)(__VA_ARGS__)

#define _REPR(i,n) REAPR(i,n,0)
#define REAPR(i,a,b) for(int i=int(a-1);i>=int(b);--i)
#define REPR(...) _overload3(__VA_ARGS__,REAPR,_REPR,)(__VA_ARGS__)

#define ALL(a) a.begin(),a.end()
#define rALL(a) a.rbegin(),a.rend()

#define coutALL(a) {int loop_coutALL=0;for(auto e:a) cout<<(loop_coutALL++?" ":"")<<e; cout<<endl;}
#define coutYN(a) cout<<(a?"Yes":"No")<<endl;
#define coutyn(a) cout<<(a?"yes":"no")<<endl;

#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)

const int INF=1145141919;
const int MOD=(int)1e9+7;
const double EPS=1e-12;
const int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
//const int dx[]={-1,-1,-1,0,1,1,1,0},dy[]={-1,0,1,1,1,0,-1,-1};

using vi=vector<int>;
using vvi=vector<vi>;
using vs=vector<string>;

typedef pair<int,int> pii;
typedef pair<int,string> pis;
typedef pair<string,int> psi;
typedef pair<string,string> pss;

typedef long long ll;

template<class T> ll upper(T n,T m){return (n+m-1)/m;};
template<class T> ll rounding(T n){return (long double)n+0.5;};

inline int qp(int a,ll b){int ans=1;do{if(b&1)ans=1ll*ans*a;a=1ll*a*a;}while(b>>=1);return ans;}
inline int qp(int a,ll b,int mo){int ans=1;do{if(b&1)ans=1ll*ans*a%mo;a=1ll*a*a%mo;}while(b>>=1);return ans;}

struct Arithmetic{Arithmetic(){cin.tie(0);ios::sync_with_stdio(0);cout<<fixed<<setprecision(20);}};

//#define DEBUG_LOCAL

#ifdef DEBUG_LOCAL
template<typename T> void deb(T a){cerr<<"deb: "<<a<<"ですねぇ！"<<endl;}
#define debl {cerr<<"debug: "<<__LINE__<<"行目だよーんおほほ"<<endl;}
void what_cr(){cout<<__GCC_ATOMIC_CHAR16_T_LOCK_FREE<<" ←なんだろーこの数字？"<<endl;}
void t_t(){cout
    <<endl
    <<"------------------------"<<endl
    <<"| Presented by         |"<<" Compiled "<<__FILE__<<endl
    <<"| "<<__DATE__<<" "<<__TIME__<<" |"<<endl
    <<"|        Chiharu Izumi |"<<"      to get the AC :)"<<endl
    <<"------------------------"<<endl;
}
#else
template<typename T>void deb(T a){}
#define debl ;
void what_cr(){}void t_t(){}
#endif

int ans,flag[10];
vi ori(9);

void dfs(int now,vi &num){

  if(now==9){

    int ans1=num[0]+num[1]*10+num[2]+num[3]*100+num[4]*10+num[5];
    int ans2=num[6]*100+num[7]*10+num[8];

    ans+=(ans1==ans2);

    return;

  }

  if(num[now]){

    dfs(now+1,num);
    return;

  }

  REP(i,1,10){

    if(flag[i]) continue;

    flag[i]=1;
    num[now]=i;

    dfs(now+1,num);

    flag[i]=0;
    num[now]=0;

  }


}

signed main(){

  Arithmetic Exception;

  REP(i,9){

    cin>>ori[i];

    if(ori[i]==-1) ori[i]=0;
    else flag[ori[i]]=1;
  }

  dfs(0,ori);

  cout<<ans<<endl;

  return 0;

}


```