/** Micro Mezz Macro Flation -- Overheated Economy ., Last Update: Mar. 3th 2013 **/ //{      /** Header .. **/ //{   #define LOCAL      #include <functional>   #include <algorithm>   #include <iostream>   #include <fstream>   #include <sstream>   #include <iomanip>   #include <numeric>   #include <cstring>   #include <climits>   #include <cassert>   #include <cstdio>   #include <string>   #include <vector>   #include <bitset>   #include <queue>   #include <stack>   #include <cmath>   #include <ctime>   #include <list>   #include <set>   #include <map>      //#include <tr1/unordered_set>   //#include <tr1/unordered_map>   //#include <array>      using namespace std;      #define REP(i, n) for (int i=0;i<int(n);++i)   #define FOR(i, a, b) for (int i=int(a);i<int(b);++i)   #define DWN(i, b, a) for (int i=int(b-1);i>=int(a);--i)   #define REP_1(i, n) for (int i=1;i<=int(n);++i)   #define FOR_1(i, a, b) for (int i=int(a);i<=int(b);++i)   #define DWN_1(i, b, a) for (int i=int(b);i>=int(a);--i)   #define REP_C(i, n) for (int n____=int(n),i=0;i<n____;++i)   #define FOR_C(i, a, b) for (int b____=int(b),i=a;i<b____;++i)   #define DWN_C(i, b, a) for (int a____=int(a),i=b-1;i>=a____;--i)   #define REP_N(i, n) for (i=0;i<int(n);++i)   #define FOR_N(i, a, b) for (i=int(a);i<int(b);++i)   #define DWN_N(i, b, a) for (i=int(b-1);i>=int(a);--i)   #define REP_1_C(i, n) for (int n____=int(n),i=1;i<=n____;++i)   #define FOR_1_C(i, a, b) for (int b____=int(b),i=a;i<=b____;++i)   #define DWN_1_C(i, b, a) for (int a____=int(a),i=b;i>=a____;--i)   #define REP_1_N(i, n) for (i=1;i<=int(n);++i)   #define FOR_1_N(i, a, b) for (i=int(a);i<=int(b);++i)   #define DWN_1_N(i, b, a) for (i=int(b);i>=int(a);--i)   #define REP_C_N(i, n) for (int n____=(i=0,int(n));i<n____;++i)   #define FOR_C_N(i, a, b) for (int b____=(i=0,int(b);i<b____;++i)   #define DWN_C_N(i, b, a) for (int a____=(i=b-1,int(a));i>=a____;--i)   #define REP_1_C_N(i, n) for (int n____=(i=1,int(n));i<=n____;++i)   #define FOR_1_C_N(i, a, b) for (int b____=(i=1,int(b);i<=b____;++i)   #define DWN_1_C_N(i, b, a) for (int a____=(i=b,int(a));i>=a____;--i)      #define ECH(it, A) for (__typeof(A.begin()) it=A.begin(); it != A.end(); ++it)   #define REP_S(i, str) for (char*i=str;*i;++i)   #define REP_L(i, hd, nxt) for (int i=hd;i;i=nxt[i])   #define REP_G(i, u) REP_L(i,hd[u],suc)   #define DO(n) for ( int ____n ## __line__ = n; ____n ## __line__ -- ; )   #define REP_2(i, j, n, m) REP(i, n) REP(j, m)   #define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)   #define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)   #define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)   #define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)   #define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)      #define ALL(A) A.begin(), A.end()   #define LLA(A) A.rbegin(), A.rend()   #define CPY(A, B) memcpy(A, B, sizeof(A))   #define INS(A, P, B) A.insert(A.begin() + P, B)   #define ERS(A, P) A.erase(A.begin() + P)   #define BSC(A, x) (lower_bound(ALL(A), x) - A.begin())   #define CTN(T, x) (T.find(x) != T.end())   #define SZ(A) int((A).size())   #define PB push_back   #define MP(A, B) make_pair(A, B)   #define PTT pair<T, T>   #define fi first   #define se second      #define Rush for(int ____T=RD(); ____T--;)      #define Display(A, n, m) {                          REP(i, n){                                         REP(j, m) cout << A[i][j] <<    ;                  cout << endl;                    }                             }      #define Display_1(A, n, m) {            REP_1(i, n){                                     REP_1(j, m) cout << A[i][j] <<    ;          cout << endl;                    }                             }      #pragma comment(linker,  /STACK:36777216 )   //#pragma GCC optimize ( O2 )      string __file__(){       string res = __FILE__;       int r = SZ(res) - 1; while (res[r] !=   . ) --r;       int l = r - 1; while (res[l] !=     ) --l; ++l;       return res.substr(l, r-l);   }      void Exec(string a, string b, string c){       if (b.empty()) b = __file__();       string cmd = a +     + b +  .  + c;       system(cmd.c_str());   }      void Ruby(string file =   ){Exec( ruby , file,  rb );}   void Python(string file =   ){Exec( python , file,  py );}   void Haskell(string file =   ){Exec( runghc , file,  hs );}   void Pascal(string file =   ){Exec( pascal , file,  pas );}   void Ocaml(string file =   ){Exec( ocaml , file,  ml );}      typedef long long LL;   //typedef long double DB;   typedef double DB;   typedef unsigned UINT;   typedef unsigned long long ULL;      typedef vector<int> VI;   typedef vector<char> VC;   typedef vector<string> VS;   typedef vector<LL> VL;   typedef vector<DB> VF;   typedef set<int> SI;   typedef set<string> SS;   typedef map<int, int> MII;   typedef map<string, int> MSI;   typedef pair<int, int> PII;   typedef pair<LL, LL> PLL;   typedef vector<PII> VII;   typedef vector<VI> VVI;   typedef vector<VII> VVII;      template<class T> inline T& RD(T &);   template<class T> inline void OT(const T &);   //inline int RD(){int x; return RD(x);}   inline LL RD(){LL x; return RD(x);}   inline DB& RF(DB &);   inline DB RF(){DB x; return RF(x);}   inline char* RS(char *s);   inline char& RC(char &c);   inline char RC();   inline char& RC(char &c){scanf(  %c , &c); return c;}   inline char RC(){char c; return RC(c);}   //inline char& RC(char &c){c = getchar(); return c;}   //inline char RC(){return getchar();}      template<class T> inline T& RDD(T &x){       char c; for (c = getchar(); c <  - ; c = getchar());       if (c ==  - ){x =  0  - getchar(); for (c = getchar();  0  <= c && c <=  9 ; c = getchar()) x = x * 10 +  0  - c;}       else {x = c -  0 ; for (c = getchar();  0  <= c && c <=  9 ; c = getchar()) x = x * 10 + c -  0 ;}       return x;   }      inline LL RDD(){LL x; return RDD(x);}      template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}   template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}   template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}   template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}   template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}   template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}   template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}   template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}   template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}   template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}   template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}   template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}   inline char& RC(char &a, char &b){RC(a), RC(b); return a;}   inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}   inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}   inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}   inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}   inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}   inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}   inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}   inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}   inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}   inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}   inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}   inline void RS(char *s1, char *s2){RS(s1), RS(s2);}   inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}   template<class T0,class T1>inline void RDD(T0&a, T1&b){RDD(a),RDD(b);}   template<class T0,class T1,class T2>inline void RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c);}      template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}   template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}   template<class T> inline void CLR(T &A){A.clear();}      template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}   template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}   template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}   template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}   template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}   template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}   template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}   template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}   template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}   template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}   template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}   template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}   template<class T> inline void CLR(priority_queue<T, vector<T>, less<T> > &Q){while (!Q.empty()) Q.pop();}   template<class T> inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q){while (!Q.empty()) Q.pop();}   template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}         template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}   template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}   template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}   template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}   template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}   template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}   template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}      template<class T> inline bool EPT(T &a){return a.empty();}   template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}   template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}   template<class T> inline T& UNQ(T &A){A.resize(unique(ALL(SRT(A)))-A.begin());return A;}      template<class T, class C> inline T& SRT(T &A, C B){sort(ALL(A), B); return A;}      //}      /** Constant List .. **/ //{      const int MOD = int(1e9) + 7;   //int MOD = 99990001;   const int INF = 0x3f3f3f3f;   const LL INFF = 0x3f3f3f3f3f3f3f3fLL;   const DB EPS = 1e-9;   const DB OO = 1e20;   const DB PI = acos(-1.0); //M_PI;      const int dx[] = {-1, 0, 1, 0};   const int dy[] = {0, 1, 0, -1};      const int dx8[] = {-1, 0, 1, 0, -1, -1, 1, 1};   const int dy8[] = {0, 1, 0, -1, -1, 1, -1, 1};      //}      /** Add On .. **/ //{   // <<=  0. Nichi Joo ., //{   template<class T> inline void checkMin(T &a,const T b){if (b<a) a=b;}   template<class T> inline void checkMax(T &a,const T b){if (a<b) a=b;}   template<class T> inline void checkMin(T &a, T &b, const T x){checkMin(a, x), checkMin(b, x);}   template<class T> inline void checkMax(T &a, T &b, const T x){checkMax(a, x), checkMax(b, x);}   template <class T, class C> inline void checkMin(T& a, const T b, C c){if (c(b,a)) a = b;}   template <class T, class C> inline void checkMax(T& a, const T b, C c){if (c(a,b)) a = b;}   template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}   template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}   template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}   template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}   template<class T> inline T sqr(T a){return a*a;}   template<class T> inline T cub(T a){return a*a*a;}   inline int ceil(int x, int y){return (x - 1) / y + 1;}   inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}   inline int sgn(DB x, DB y){return sgn(x - y);}      inline DB cot(DB x){return (DB)1/tan(x);};   inline DB sec(DB x){return (DB)1/cos(x);};   inline DB csc(DB x){return (DB)1/sin(x);};      //}   // <<=  1. Bitwise Operation ., //{   namespace BO{      inline bool _1(int x, int i){return bool(x&1<<i);}   inline bool _1(LL x, int i){return bool(x&1LL<<i);}   inline LL _1(int i){return 1LL<<i;}   inline LL _U(int i){return _1(i) - 1;};      inline int reverse_bits(int x){       x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);       x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);       x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);       x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);       x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);       return x;   }      inline LL reverse_bits(LL x){       x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);       x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);       x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);       x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);       x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);       x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);       return x;   }      template<class T> inline bool odd(T x){return x&1;}   template<class T> inline bool even(T x){return !odd(x);}   template<class T> inline T low_bit(T x) {return x & -x;}   template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}   template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}   template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}      inline int clz(int x){return __builtin_clz(x);}   inline int clz(LL x){return __builtin_clzll(x);}   inline int ctz(int x){return __builtin_ctz(x);}   inline int ctz(LL x){return __builtin_ctzll(x);}   inline int lg2(int x){return !x ? -1 : 31 - clz(x);}   inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}   inline int low_idx(int x){return !x ? -1 : ctz(x);}   inline int low_idx(LL x){return !x ? -1 : ctz(x);}   inline int high_idx(int x){return lg2(x);}   inline int high_idx(LL x){return lg2(x);}   inline int parity(int x){return __builtin_parity(x);}   inline int parity(LL x){return __builtin_parityll(x);}   inline int count_bits(int x){return __builtin_popcount(x);}   inline int count_bits(LL x){return __builtin_popcountll(x);}      } using namespace BO;//}   // <<=  2. Number Theory .,//{   namespace NT{   inline LL __lcm(LL a, LL b){return a*b/__gcd(a,b);}   inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}   inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}   inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}   inline int dff(int a, int b){a -= b; if (a < 0) a  += MOD; return a;}   inline void MUL(int &a, int b){a = (LL)a * b % MOD;}   inline int pdt(int a, int b){return (LL)a * b % MOD;}      inline int sum(int a, int b, int c){return sum(sum(a, b), c);}   inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}   inline int pdt(int a, int b, int c){return pdt(pdt(a, b), c);}   inline int pdt(int a, int b, int c, int d){return pdt(pdt(pdt(a, b), c), d);}      inline int pow(int a, LL b){       int c(1); while (b){           if (b&1) MUL(c, a);           MUL(a, a), b >>= 1;       }       return c;   }      template<class T> inline T pow(T a, LL b){       T c(1); while (b){           if (b&1) c *= a;           a *= a, b >>= 1;       }       return c;   }      template<class T> inline T pow(T a, int b){       return pow(a, (LL)b);   }      inline int _I(int b){       int a = MOD, x1 = 0, x2 = 1, q;       while (true){           q = a / b, a %= b;           if (!a) return (x2 + MOD) % MOD;           DEC(x1, pdt(q, x2));              q = b / a, b %= a;           if (!b) return (x1 + MOD) % MOD;           DEC(x2, pdt(q, x1));       }   }      inline void DIV(int &a, int b){MUL(a, _I(b));}   inline int qtt(int a, int b){return pdt(a, _I(b));}      struct Int{       int val;          operator int() const{return val;}          Int(int val = 0):val(val){           //val %= MOD; if (val < 0) val += MOD;       }       inline Int& operator +=(const int& rhs){           INC(val, rhs);           return *this;       }       inline Int operator +(const int& rhs) const{           return sum(val, rhs);       }       inline Int& operator -=(const int& rhs){           DEC(val, rhs);           return *this;       }       inline Int operator -(const int& rhs) const{           return dff(val, rhs);       }       inline Int& operator *=(const int& rhs){           MUL(val, rhs);           return *this;       }       inline Int operator *(const int& rhs) const{           return pdt(val, rhs);       }       inline Int& operator /=(const int& rhs){           DIV(val, rhs);           return *this;       }       inline Int operator /(const int& rhs) const{           return qtt(val, rhs);       }   };      const int PMAX = 1;   VI P; bitset<PMAX> isP;   void sieve(){       FOR(i, 2, PMAX){           if (!isP[i]) P.PB(i);           for (int j=0;j<SZ(P)&&i*P[j]<PMAX;++j){               isP[i*P[j]]=1; if (!(i%P[j])) break;           }       }   }      inline int phi(int n){       int res = n; for (int i=2;sqr(i)<=n;++i) if (!(n%i)){           DEC(res, qtt(res, i));           do{n /= i;} while(!(n%i));       }       if (n != 1)           DEC(res, qtt(res, n));       return res;   }      } using namespace NT;//}   // <<=  7. Matrix Theory .,//{   namespace MT{          const int N = 100;       int n = 0;          typedef int rec;          struct matrix{           rec d[N][N];              void init(rec e = 0){RST(d); if(e) REP(i, n) d[i][i] = e;}           matrix(rec e = 0){init(e);}              matrix operator *(const matrix &rhs) const{               matrix res; //REP_3(i, j, k, n, n, n) res.d[i][j] += d[i][k] * rhs.d[k][j];               REP_2(i, j, n, n){                   LL tmp = 0; REP(k, n) tmp += (LL) d[i][k] * rhs.d[k][j];                   res.d[i][j] = tmp % MOD;               }               return res;           }              matrix& operator *=(const matrix& rhs){(*this) = (*this) * rhs;}              inline int res(){               int res = 0;               REP(i, n) INC(res, d[0][i]);               //REP_2(i, j, n, n) INC(res, d[i][j]);               return res;           }       };          /*inline matrix pow_sum(const matrix& a, LL nn){           if (nn == 1) return matrix(1);           matrix t; REP_2(i, j, n, n) t.d[i][j] = t.d[i][j+n] = a.d[i][j];           FOR_C(i, n, n*2) t.d[i][i] = 1; n <<= 1; t = pow(t, nn), n >>= 1;           REP_2(i, j, n, n) t.d[i][j] = t.d[i][j+n];           return t;       }*/          inline matrix pow_sum(const matrix& a, LL nn){           if (nn == 1) return matrix(1);           matrix t; REP_2(i, j, n, n) t.d[i][j] = a.d[i][j];           REP(i, n) t.d[i][i+n] = t.d[i+n][i+n] = 1; n <<= 1; t = pow(t, nn), n >>= 1;           REP_2(i, j, n, n) t.d[i][j] = t.d[i][j+n];           return t;       }          template<class T> T pow_sum(T a, LL nn){           int _n = n; n = 1; matrix t; t.d[0][0] = a;           t = pow_sum(t, nn), n = _n;           return t.d[0][0];       }      } //using namespace MT;//}   // <<=  8. Stringology .,//{   namespace SL{       namespace KMP{              void calc_pi(const char *P, int n, int *pi){               for (int i = 1, j = pi[0] = -1; i < n; ++i){                   while (j >= 0 && P[i] != P[j+1]) j = pi[j];                   if (P[i] == P[j+1]) ++j;                   pi[i] = j;               }               //REP(i, n) cout << pi[i] <<    ; cout << endl;           }              bool run(const char *T, int n, const char *P, int m, const int *pi){               for (int i = 0, j = -1; i < n; ++i){                   while (j >= 0 && T[i] != P[j+1]) j = pi[j];                   if (T[i] == P[j+1]) ++j;                   if (j == m - 1) return true;               }               return false;           }          } //using namespace KMP;          namespace Z{           void calc_z(const char *P, int n, int *z){                  z[0] = n;                  for (int i = 1, l = 0, r = 0; i < n; ++i){                   if (i > r){                       for(l = r = i; r < n && P[r] == P[r - l];) ++r;                       z[i] = r - l, --r;                   }                   else {                       if (z[i - l] < r - i + 1) z[i] = z[i - l];                       else {                           for (l = i;r < n && P[r] == P[r - l];) ++r;                           z[i] = r - l, --r;                       }                   }               }                  //REP(i, n) cout << z[i] <<    ; cout << endl;           }              int run(const char *T, int n, const char *P, int m, const int *z){                  int ex; REP_C_N(ex, min(n, m)) if (T[ex] != P[ex]) break;                  int res = ex == m;                  for (int i = 1, l = 0, r = 0; i < n; ++i){                   if (i > r){                       for (l = r = i; r < n && T[r] == P[r - l];) ++r;                       ex = r - l, --r;                   }                   else {                       if (z[i - l] < r - i + 1) ex = z[i - l];                       else {                           for (l = i; r < n && T[r] == P[r - l];) ++r;                           ex = r - l, --r;                       }                   }                   if (ex == m) ++res;               }                  return res;           }       } //using namespace Z;          void Manacher(char s[], int n, int p[]){           const int NN = 0;           static char ss[NN*2+2]; int nn = 2*n+2;           ss[0] =  $ , ss[nn-1] =  # , ss[nn] = 0;           REP(i, n) ss[i*2+1] = # , ss[i*2+2] = s[i];           int mx = 0, id = 0; FOR(i, 1, nn){               p[i] = mx > i ? min(p[2*id-i], mx - i) : 1;               while (ss[i+p[i]] == ss[i-p[i]]) ++p[i];               if (i + p[i] > mx) mx = i + p[i], id = i;           }       }      } //using namespace SL;//}   // <<=  9. Comutational Geometry .,//{   namespace CG{      struct Po; struct Line; struct Seg;      struct Po{       DB x, y; Po(DB _x=0, DB _y=0):x(_x), y(_y){}       friend istream& operator >>(istream& in, Po &p){return in >> p.x >> p.y;}       friend ostream& operator <<(ostream& out, Po p){return out <<  (  << p.x <<  ,   << p.y <<  ) ;}       bool operator ==(const Po& r)const{return !sgn(x-r.x) && !sgn(y-r.y);};       bool operator !=(const Po& r)const{return sgn(x-r.x) || sgn(y-r.y);}       Po operator +(const Po& r)const{return Po(x+r.x, y+r.y);}       Po operator -(const Po& r)const{return Po(x-r.x, y-r.y);}       Po operator *(DB k)const{return Po(x*k,y*k);}       Po operator /(DB k)const{return Po(x/k,y/k);}       DB operator *(const Po&) const;       DB operator ^(const Po&) const;          bool operator <(const Po &r) const{return sgn(x,r.x)<0||!sgn(x,r.x)&&sgn(y,r.y)<0;}       Po operator -()const{return Po(-x,-y);}       Po& operator +=(const Po &r){x+=r.x,y+=r.y;return *this;}       Po& operator -=(const Po &r){x-=r.x,y-=r.y;return *this;}       Po& operator *=(DB k){x*=k,y*=k;return*this;}       Po& operator /=(DB k){x/=k,y/=k;return*this;}          DB length_sqr()const{return sqr(x)+sqr(y);}       DB length()const{return sqrt(length_sqr());}       Po unit()const{return *this/length();}       bool dgt()const{return !sgn(x)&&!sgn(y);}       DB atan()const{return atan2(y,x);}       void rotate(DB alpha, const Po& o = Po()){           x -= o.x, y -= o.y;           (*this) = Po(x * cos(alpha) - y * sin(alpha), y * cos(alpha) + x * sin(alpha)) + o;       }          void input(){RF(x,y);}   };      Po operator *(DB k, Po a){return a * k;}      #define innerProduct dot   #define scalarProduct dot   #define outerProduct det   #define crossProduct det      inline DB dot(const DB &x1, const DB &y1, const DB &x2, const DB &y2){return x1 * x2 + y1 * y2;}   inline DB dot(const Po &a, const Po &b){return dot(a.x, a.y, b.x, b.y);}   inline DB dot(const Po &p0, const Po &p1, const Po &p2){return dot(p1 - p0, p2 - p0);}      inline DB det(const DB &x1, const DB &y1, const DB &x2, const DB &y2){return x1 * y2 - x2 * y1;}   inline DB det(const Po &a, const Po &b){return det(a.x, a.y, b.x, b.y);}   inline DB det(const Po &p0, const Po &p1, const Po &p2){return det(p1 - p0, p2 - p0);}      template<class T1, class T2> inline int dett(const T1 &x, const T2 &y){return sgn(det(x, y));}   template<class T1, class T2> inline int dott(const T1 &x, const T2 &y){return sgn(dot(x, y));}   template<class T1, class T2, class T3> inline int dett(const T1 &x, const T2 &y, const T3 &z){return sgn(det(x, y, z));}   template<class T1, class T2, class T3> inline int dott(const T1 &x, const T2 &y, const T3 &z){return sgn(dot(x, y, z));}   template<class T1, class T2, class T3, class T4> inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(det(x, y, z, w));}   template<class T1, class T2, class T3, class T4> inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(dot(x, y, z, w));}            inline int dist_sqr(const int &x1, const int &y1, const int &x2, const int &y2){       return sqr(x2-x1) + sqr(y2-y1);   }      inline DB dist_sqr(const DB &x, const DB &y){return sqr(x) + sqr(y);}   inline DB dist_sqr(const DB &x, const DB &y, const DB &z){return sqr(x) + sqr(y) + sqr(z);}   inline DB dist_sqr(const Po &a, const Po &b){return sqr(a.x - b.x) + sqr(a.y - b.y);}      template<class T1, class T2> inline DB dist(const T1 &x, const T2 &y){return sqrt(dist_sqr(x, y));}   template<class T1, class T2, class T3> inline DB dist(const T1 &x, const T2 &y, const T3 &z){return sqrt(dist_sqr(x, y, z));}      DB Po::operator *(const Po &r)const{return dot(*this, r);}   DB Po::operator ^(const Po &r)const{return det(*this, r);}      struct Line{       Po a, b;          Line(DB x0=0, DB y0=0, DB x1=0, DB y1=0):a(Po(x0, y0)), b(Po(x1, y1)){}       Line(const Po &a, const Po &b):a(a), b(b){}       Line(const Line &l):a(l.a), b(l.b){}          friend ostream& operator <<(ostream& out, Line p){return out << p.a <<  -  << p.b;}       Line operator +(Po x)const{return Line(a + x, b + x);}       DB length()const{return (b-a).length();}       bool dgt()const{return (b-a).dgt();}       void input(){a.input(), b.input();}          int side(const Po& p){return dett(a, b, p);}       bool same_side(const Po& p1, const Po& p2){return side(p1) == side(p2);}       void getequation(DB& A, DB& B, DB& C) const{A = a.y - b.y, B = b.x - a.x, C = det(a, b);}   };      struct Seg: Line{   };      inline DB dot(const Line &l1, const Line &l2){return dot(l1.b - l1.a, l2.b - l2.a);}   inline DB det(const Line &l1, const Line &l2){return det(l1.b - l1.a, l2.b - l2.a);}      inline DB dist_sqr(const Po &p, const Line &l){Po v0 = l.b - l.a, v1 = p - l.a; return sqr(fabs(det(v0, v1))) / v0.length_sqr();}   inline DB dist_sqr(const Po &p, const Seg &l){       Po v0 = l.b - l.a, v1 = p - l.a, v2 = p - l.b;       if (sgn(dot(v0, v1)) * sgn(dot(v0, v2)) <= 0) return dist_sqr(p, Line(l));       else return min(v1.length_sqr(), v2.length_sqr());   }   inline DB dist_sqr(Line l, Po p){return dist_sqr(p, l);}   inline DB dist_sqr(Seg l, Po p){return dist_sqr(p, l);}   inline DB dist_sqr(Line l1, Line l2){       if (sgn(det(l1, l2)) != 0) return 0;       return dist_sqr(l1.a, l2);   }   inline DB dist_sqr(Line l1, Seg l2){       Po v0 = l1.b - l1.a, v1 = l2.a - l1.a, v2 = l2.b - l1.a; DB c1 = det(v0, v1), c2 = det(v0, v2);       return sgn(c1) != sgn(c2) ? 0 : sqr(min(fabs(c1), fabs(c2))) / v0.length_sqr();   }      bool isIntersect(Seg l1, Seg l2){          if (l1.a == l2.a || l1.a == l2.b || l1.b == l2.a || l1.b == l2.b) return true;          return           min(l1.a.x, l1.b.x) <= max(l2.a.x, l2.b.x) &&           min(l2.a.x, l2.b.x) <= max(l1.a.x, l1.b.x) &&           min(l1.a.y, l1.b.y) <= max(l2.a.y, l2.b.y) &&           min(l2.a.y, l2.b.y) <= max(l1.a.y, l1.b.y) &&       sgn( det(l1.a, l2.a, l2.b) ) * sgn( det(l1.b, l2.a, l2.b) ) <= 0 &&       sgn( det(l2.a, l1.a, l1.b) ) * sgn( det(l2.b, l1.a, l1.b) ) <= 0;      }      inline DB dist_sqr(Seg l1, Seg l2){       if (isIntersect(l1, l2)) return 0;       else return min(dist_sqr(l1.a, l2), dist_sqr(l1.b, l2), dist_sqr(l2.a, l1), dist_sqr(l2.b, l1));   }      inline bool isOnSide(const Po &p, const Seg &l){       return p == l.a || p == l.b;   }      inline bool isOnSeg(const Po &p, const Seg &l){       return sgn(det(p, l.a, l.b)) == 0 &&           sgn(l.a.x, p.x) * sgn(l.b.x, p.x) <= 0 && sgn(l.a.y, p.y) * sgn(l.b.y, p.y) <= 0;   }      inline bool isOnSegg(const Po &p, const Seg &l){       return sgn(det(p, l.a, l.b)) == 0 &&           sgn(l.a.x, p.x) * sgn(l.b.x, p.x) < 0 && sgn(l.a.y, p.y) * sgn(l.b.y, p.y) < 0;   }      inline Po intersect(const Line &l1, const Line &l2){       return l1.a + (l1.b - l1.a) * (det(l2.a, l1.a, l2.b) / det(l2, l1));   }      // perpendicular foot   inline Po intersect(const Po & p, const Line &l){       return intersect(Line(p, p + Po(l.a.y - l.b.y, l.b.x - l.a.x)), l);   }      inline Po rotate(Po p, DB alpha, const Po &o = Po()){       p.rotate(alpha, o);       return p;   }      } using namespace CG;//}   //}      template<class T> int LIS(int n, T* a){       VI b; b.PB(a[0]); FOR(i, 1, n){           if (b.back() < a[i]) b.PB(a[i]);           else {               b[lower_bound(ALL(b), a[i]) - b.begin()] = a[i];           }       }       return SZ(b);   }      template<class T, class C> int LIS(int n, T* a, C cmp){       vector<T> b; b.PB(a[0]); FOR(i, 1, n){           if (cmp(b.back(), a[i])) b.PB(a[i]);           else {               b[lower_bound(ALL(b), a[i], cmp) - b.begin()] = a[i];           }       }       return SZ(b);   }         template<class T> int LISS(int n, T* a, int* pre, int& lst){       VI b; b.PB(0); pre[0] = -1; FOR(i, 1, n){           if (a[b.back()] < a[i]) pre[i] = b.back(), b.PB(i);           else {               int l = 0, r = SZ(b); while (l < r){                   int m = l + r >> 1;                   if (a[b[m]] < a[i]) l = m + 1;                   else r = m;               }               pre[i] = !r ? -1 : b[r-1];               b[r] = i;           }       }       lst = b.back();       return SZ(b);   }      template<class T, class C> int LISS(int n, T* a, int* pre, int& lst, C cmp){       VI b; b.PB(0); pre[0] = -1; FOR(i, 1, n){           if (cmp(a[b.back()], a[i])) pre[i] = b.back(), b.PB(i);           else {               int l = 0, r = SZ(b); while (l < r){                   int m = l + r >> 1;                   if (cmp(a[b[m]], a[i])) l = m + 1;                   else r = m;               }               pre[i] = !r ? -1 : b[r-1];               b[r] = i;           }       }          lst = b.back();       return SZ(b);   }      /** Miscellaneous .. **/ //{   // <<=  Random Event .. . //{   namespace RNG{   //srand((unsigned)time(NULL));   inline unsigned int rand16(){return ((rand()) << 15) ^ rand();}   inline unsigned int rand32(){return (rand16() << 16) | rand16();}   inline ULL rand64(){return ((LL)rand32() << 32) | rand32();}   inline ULL random(LL l, LL r){return l == r ? l : rand64() % (r - l) + l;}   int dice(){return rand() % 6;}   bool coin(){return bool(rand() % 2);}   } using namespace RNG;   //}   // <<=  Clock .. . //{   namespace CLOCK{   DB s0, s1, rd, k, T;   inline DB getTime(){   #ifdef LOCAL       return 1.0 * clock() / CLOCKS_PER_SEC;   #else       timeval tv;       gettimeofday(&tv, 0);       return tv.tv_sec + tv.tv_usec * 1e-6;   #endif   }      inline void st0(DB _T = 0.98){T = _T, s0 = getTime();}   inline void st1(DB _k = 1.618){k = _k, s1 = getTime();}   inline void ed1(){rd = getTime() - s1;}   inline DB elapsed(){return getTime() - s0;}   inline bool TLE(){return elapsed() + rd * k < T;}   } //using namespace CLOCK;   //}   // <<=  Temp .. . //{   namespace TMP{   template<class T> PTT operator+(const PTT &p1, const PTT &p2) {    return PTT(p1.fi + p2.fi, p1.se + p2.se);   }      template<class T> PTT operator-(const PTT &p1, const PTT &p2) {    return PTT(p1.fi - p2.fi, p1.se - p2.se);   }      template<class T> PTT operator*(const PTT &lhs, T k){       return PTT(lhs.fi * k, lhs.se * k);   }   } using namespace TMP;   //}   // <<=  Bignum ., //{   namespace BIGNUM{      const int __base = 1e8;   const int P10[] = {1, 10, int(1e2), int(1e3), int(1e4), int(1e5), int(1e6), int(1e7), int(1e8), int(1e9)};   const int MAX_BUF_SIZE = 109;   char __buf[MAX_BUF_SIZE];      class bignum{             friend istream& operator>>(istream&, bignum&);             friend ostream& operator<<(ostream&, const bignum&);             friend bignum operator +(const bignum&, const bignum&);             friend bignum operator -(const bignum&, const bignum&);             friend bignum operator *(const bignum&, const bignum&);             friend bignum operator /(const bignum&, const bignum&);             friend bignum operator %(const bignum&, const bignum&);             friend bignum operator +(const bignum&, const int&);             friend bignum operator -(const bignum&, const int&);             friend bignum operator *(const bignum&, const int&);             friend bignum operator /(const bignum&, const int&);             friend bignum operator %(const bignum&, const int&);             friend bool operator ==(const bignum&, const bignum&);             friend bool operator !=(const bignum&, const bignum&);             friend bool operator <(const bignum&, const bignum&);             friend bool operator >(const bignum&, const bignum&);             friend bool operator <=(const bignum&, const bignum&);             friend bool operator >=(const bignum&, const bignum&);             friend bool operator ==(const bignum&, const int&);             friend bool operator !=(const bignum&, const int&);             friend bool operator <(const bignum&, const int&);             friend bool operator >(const bignum&, const int&);             friend bool operator <=(const bignum&, const int&);             friend bool operator >=(const bignum&, const int&);             friend int do_comp(const bignum&, const int&);             friend int do_comp(const bignum&, const bignum&);             friend void divide(const bignum&, const bignum&, bignum&, bignum&);             friend bignum pow(bignum, int);             friend bignum pow(int, int);       public:           inline bignum(){};           inline bignum(int s){               while (s) data.PB(s%__base), s/=__base;               if (data.empty()) data.PB(0);           }              inline bignum(long long s){               while (s) data.PB(int(s%__base)), s/=__base;               if (data.empty()) data.PB(0);           }              inline bignum(string s){               int t, i; CLR(data);               for (i=int(s.size())-8;i>0;i-=8){                   istringstream(s.substr(i, 8)) >> t;                   data.PB(t);               }               istringstream(s.substr(0, i+8)) >> t;               data.PB(t);           }              void input(){               CLR(data); RS(__buf); int t = 0, c = 0;               DWN(i, strlen(__buf), 0){                   t += P10[c] * (int(__buf[i]) -  0 ), ++c;                   if (c == 8) data.PB(t), c = t = 0;               }               if (c) data.PB(t);           }              void operator =(const int);           void operator =(const string);           void operator =(const bignum);           bignum& operator +=(const bignum&);           bignum& operator -=(const bignum&);           bignum& operator *=(const bignum&);           bignum& operator /=(const bignum&);           bignum& operator %=(const bignum&);           bignum& operator +=(const int&);           bignum& operator -=(const int&);           bignum& operator *=(const int&);           bignum& operator /=(const int&);           bignum& operator %=(const int&);           bool undefined();           int do_try(const int&);           int do_try(const bignum&);           void do_trim();           list<int> data;          int size(){           list<int>::iterator it; int res = 0;           for (it=data.begin(); it!=data.end();it++)               res += 8;           it--;           if (*it >= 10000) {               if ( (*it) >= 1000000) {if (*it >=10000000) ; else res--;}               else {if ((*it) >= 100000) res-=2; else res-=3;}           }           else               if ( (*it) >= 100) {if (*it >=1000) res-=4; else res-=5;}               else {if ((*it) >= 10) res-=6; else res-=7;}              return res;       }          void do_reserve(int a){           if (a <= 0) return;           list<int>::iterator it;           for (it=data.begin(); it!=data.end() && a>0; it++) a-=8;           if (it == data.end() && a>=0) return;           a+=8, it--; int f = 1;           for (int i=0;i<a;i++) f *= 10; (*it) %= f;           data.erase(++it, data.end());           do_trim();       }   };      inline void bignum::operator =(const bignum a){       data.clear();       for (list<int>::const_iterator i=a.data.begin();i!=a.data.end();i++){           data.PB(*i);       }   }   inline void bignum::operator =(const string a){       (*this) = bignum(a);   }   inline void bignum::operator =(const int a){       (*this) = bignum(a);   }      inline istream& operator>>(istream& input, bignum& a){       string s; int t, i; input >> s; a.data.clear();       for (i=int(s.size())-8;i>0;i-=8){           istringstream(s.substr(i, 8)) >> t;           a.data.PB(t);       }       istringstream(s.substr(0, i+8)) >> t;       a.data.PB(t);       return input;   }      inline ostream& operator<<(ostream& output, const bignum& a){       list<int>::const_reverse_iterator i=a.data.rbegin();       output << *i;       for (i++;i!=a.data.rend();i++){           if (*i >= 10000) {               if (*i >= 1000000) {if (*i>=10000000) cout << *i; else cout << 0 << *i;}               else {if (*i>=100000) cout <<  00  << *i; else cout <<  000  << *i;}           }           else {               if (*i >= 100) {if (*i>=1000)  cout <<  0000  << *i; else cout <<  00000  << *i;}               else { if (*i>=10) cout <<  000000  << *i; else cout <<  0000000  << *i;}           }       }       return output;   }      inline bool bignum::undefined(){       return data.empty();   }      inline int do_comp(const bignum& a, const bignum& b){       if (a.data.size()<b.data.size()) return -1; if (a.data.size()>b.data.size()) return 1;       list<int>::const_reverse_iterator i; list<int>::const_reverse_iterator j;       for (i=a.data.rbegin(),j=b.data.rbegin(); j!=b.data.rend(); i++,j++){           if (*i<*j) return -1;              //!!!!           if (*i>*j) return 1;       }       return 0;   }   inline int do_comp(const bignum& a, const int& b){       return do_comp(a, bignum(b));   }      inline bool operator ==(const bignum& a, const bignum& b){       return do_comp(a, b) == 0;   }   inline bool operator !=(const bignum& a, const bignum& b){       return do_comp(a, b) != 0;   }   inline bool operator <(const bignum& a, const bignum& b){       return do_comp(a, b) == -1;   }   inline bool operator >(const bignum& a, const bignum& b){       return do_comp(a, b) == 1;   }   inline bool operator <=(const bignum& a, const bignum& b){       return do_comp(a, b) != 1;   }   inline bool operator >=(const bignum& a, const bignum& b){       return do_comp(a, b) != -1;   }      inline bool operator ==(const bignum& a, const int& b){       return do_comp(a, b) == 0;   }   inline bool operator !=(const bignum& a, const int& b){       return do_comp(a, b) != 0;   }   inline bool operator <(const bignum& a, const int& b){       return do_comp(a, b) == -1;   }   inline bool operator >(const bignum& a, const int& b){       return do_comp(a, b) == 1;   }   inline bool operator <=(const bignum& a, const int& b){       return do_comp(a, b) != 1;   }   inline bool operator >=(const bignum& a, const int& b){       return do_comp(a, b) != -1;   }      inline void bignum::do_trim(){       while (data.size()>1&&data.back()==0) data.pop_back();   }      inline bignum& bignum::operator +=(const bignum& a){       list<int>::iterator i; list<int>::const_iterator j; int t = 0;       for (i=data.begin(),j=a.data.begin(); i!=data.end()&&j!=a.data.end(); i++,j++){           *i+=*j+t; t=*i/__base; *i%=__base;       }       while (i!=data.end()) {*i+=t; t=*i/__base; *i%=__base; i++;}       while (j!=a.data.end()) {data.PB(t+*j); t=data.back()/__base; data.back()%=__base; j++;}       if (t!=0) data.PB(t);       return *this;   }      inline bignum& bignum::operator -=(const bignum& a){       list<int>::iterator i; list<int>::const_iterator j; int t = 0;       for (i=data.begin(),j=a.data.begin(); j!=a.data.end(); i++,j++){           *i -= t+*j; if (*i>=0) t=0; else *i+=__base, t=1;       }       while (i!=data.end()) {*i-=t; if (*i>=0) t=0;else *i+=__base, t=1; i++;}       (*this).do_trim();       return *this;   }      inline bignum& bignum::operator +=(const int& a){       return (*this)+=bignum(a);   }      inline bignum& bignum::operator -=(const int& a){       return (*this)-=bignum(a);   }      inline bignum operator +(const bignum& a, const bignum& b){       list<int>::const_iterator i, j; bignum c; int t = 0;       for (i=a.data.begin(),j=b.data.begin(); i!=a.data.end()&&j!=b.data.end(); i++,j++){           c.data.PB(t+*i+*j);           t=c.data.back()/__base; c.data.back()%=__base;       }       while (i!=a.data.end()) {c.data.PB(t+*i); t=c.data.back()/__base; c.data.back()%=__base; i++;}       while (j!=b.data.end()) {c.data.PB(t+*j); t=c.data.back()/__base; c.data.back()%=__base; j++;}       if (t!=0) c.data.PB(t);       return c;   }      inline bignum operator -(const bignum& a, const bignum& b){       list<int>::const_iterator i, j; bignum c; int t = 0;       for (i=a.data.begin(),j=b.data.begin(); j!=b.data.end(); i++,j++){           t = *i - t;           if (t>=*j) c.data.PB(t-*j), t=0;           else c.data.PB(t+__base-*j), t=1;       }       while (i!=a.data.end()) {t=*i-t; if (t>=0) c.data.PB(t), t=0;else c.data.PB(t+__base), t=1; i++;}       c.do_trim();       return c;   }      inline bignum operator *(const bignum& a, const bignum& b){       list<int>::const_iterator i, j; list<int>::iterator k, kk; bignum c; long long t = 0;          for (int i=0;i<a.data.size()+b.data.size();i++) c.data.PB(0);       for (i=a.data.begin(),k=c.data.begin(); i!=a.data.end(); i++,k++){           for (j=b.data.begin(),kk=k; j!=b.data.end(); j++,kk++){               t+=(long long)(*i)*(*j)+(*kk);               *kk=int(t%__base); t/=__base;           }           *kk+=t; t=0;       }       c.do_trim();       return c;   }      inline int bignum::do_try(const bignum& a){       int l = 1, r = 99999999, m, t;       while (l+2<r){           m = (l + r) / 2;           t = do_comp(*this, a*bignum(m));           if (t==0) return m;           if (t<0) r = m - 1;           else l = m;       }       while (do_comp(*this, a*bignum(r))<0) r--;       return r;   }      inline void divide(const bignum& a, const bignum& b, bignum& d, bignum& r){       list<int>::const_reverse_iterator i = a.data.rbegin(); int t;       d = bignum(0); r = bignum(0);       do {           while (r<b&&i!=a.data.rend()){d.data.push_front(0);r.data.push_front(*i);r.do_trim();i++;}           if (r>=b){               t = r.do_try(b); d.data.front() = t;               r-=(b*bignum(t));           }       } while (i!=a.data.rend());       d.do_trim();   }      inline bignum operator /(const bignum& a, const bignum& b){       bignum d, r;       divide(a, b, d, r);       return d;   }      inline bignum operator %(const bignum& a, const bignum& b){       bignum d, r;       divide(a, b, d, r);       return r;   }      inline bignum operator +(const bignum& a, const int& b){       return a+bignum(b);   }      inline bignum operator -(const bignum& a, const int& b){       return a-bignum(b);   }      inline bignum operator *(const bignum& a, const int& b){       return a*bignum(b);   }      inline bignum operator /(const bignum& a, const int& b){       return a/bignum(b);   }      inline bignum operator %(const bignum& a, const int& b){       return a%bignum(b);   }      inline bignum& bignum::operator *=(const bignum& a){       (*this) = (*this) * a;       return *this;   }      inline bignum& bignum::operator /=(const bignum& a){       (*this) = (*this) / a;       return *this;   }      inline bignum& bignum::operator %=(const bignum& a){       (*this) = (*this) % a;       return *this;   }      inline bignum& bignum::operator *=(const int& a){       return (*this)*=bignum(a);   }      inline bignum& bignum::operator /=(const int& a){       return (*this)/=bignum(a);   }      inline bignum& bignum::operator %=(const int& a){       return (*this)%=bignum(a);   }      inline bignum pow(bignum a,int b){       bignum c(1);       while (b!=0) {           if (b&1) c *= a;           a = a * a; b >>= 1;       }       return c;   }   inline bignum pow(int a, int b){       return pow(bignum(a), b);   }      } //using namespace BIGNUM;   //}   //}      /** I/O Accelerator Interface .. **/ //{   template<class T> inline T& RD(T &x){       //cin >> x;       //scanf( %d , &x);       char c; for (c = getchar(); c <  0 ; c = getchar()); x = c -  0 ; for (c = getchar();  0  <= c && c <=  9 ; c = getchar()) x = x * 10 + c -  0 ;       //char c; c = getchar(); x = c -  0 ; for (c = getchar(); c >=  0 ; c = getchar()) x = x * 10 + c -  0 ;       return x;   }      inline DB& RF(DB &x){       //cin >> x;       scanf( %lf , &x);       /*char t; while ((t=getchar())==   ||t==  n ); x = t -  0 ;       while ((t=getchar())!=   &&t!=  n &&t!= . )x*=10,x+=t- 0 ;       if (t== . ){DB l=1; while ((t=getchar())!=   &&t!=  n )l*=0.1,x += (t- 0 )*l;}*/       return x;   }      inline char* RS(char *s){       //gets(s);       scanf( %s , s);       return s;   }      LL last_ans; int Case; template<class T> inline void OT(const T &x){       //printf( Case %d: %d n , ++Case, x);       printf( %lld  , x);       //printf( %d n , x);       //cout << x << endl;       //last_ans = x;   }   //}      //}/* .................................................................................................................................. */      const int N = int(2e3) + 9;      int Sun[N][N], Ray[N][N];   int n, m; VI R;      bool inGrid(int x, int y){       return x >= 0 && y >= 0 && x < n && y < m;   }      const int _D = 4, _C = 10;      int dfss(int x, int y){       if (!Ray[x][y]) return 0;       Ray[x][y] = 0; int res = 1; REP(i, 4){           int xx = x + dx[i], yy = y + dy[i];           if (inGrid(xx, yy) && Ray[xx][yy]) res += dfss(xx, yy);       }       return res;   }      int dfs(int x, int y){       Sun[x][y] = 0; int res = dfss(x, y) >= 10; REP(i, 4){           int xx = x + dx[i], yy = y + dy[i];           if (inGrid(xx, yy) && Sun[xx][yy]) res += dfs(xx, yy);       }       return res;   }      int main(){      #ifndef ONLINE_JUDGE       freopen( 01.in.txt ,  r , stdin);       //freopen( out.txt ,  w , stdout);   #endif          RD(n, m); REP_2(i, j, n, m) RD(Sun[i][j]);             REP_2(i, j, n, m) if (Sun[i][j]){           int x, y, bj1, bj2;              bj1 = bj2 = 0; REP_1(d, _D){               x = i + d, y = j; if (inGrid(x, y) && !Sun[x][y]) bj1 = 1;               x = i - d, y = j; if (inGrid(x, y) && !Sun[x][y]) bj2 = 1;           }           if (bj1 && bj2){Ray[i][j] = 1; continue;}              bj1 = bj2 = 0; REP_1(d, _D){               x = i, y = j + d; if (inGrid(x, y) && !Sun[x][y]) bj1 = 1;               x = i, y = j - d; if (inGrid(x, y) && !Sun[x][y]) bj2 = 1;           }           if (bj1 && bj2){Ray[i][j] = 1; continue;}       }          REP_2(i, j, n, m) if (Sun[i][j]){           R.PB(dfs(i, j));       }          /*REP_2(i, j, n, m){           cout << Ray[i][j];           if (j == m - 1) cout << endl;       }*/          SRT(R); cout << SZ(R) <<endl;       ECH(it, R) cout << (*it) <<    ;   }