Ultraviolet A 11255 neck133

Uva_11255

The key to applying the Burnside theorem is to find the number of immobile solutions for each replacement.

 Import  Java. Math. biginteger;  Import  Java. util. vendor;  Public   Class  Main {  Static   Int Maxd = 50 ;  Static Scanner CIN = New Using (system. In );  Static   Int  N, P, PN;  Static   Int [] A = New   Int [5], B = New   Int [5], prime = New   Int [Maxd], P = New   Int  [Maxd]; Static   Boolean [] Isprime = New   Boolean  [Maxd];  Static Biginteger [] FAC = New  Biginteger [maxd];  Static  Biginteger ans;  Public   Static   Void  Main (string [] ARGs) {prepare ();  Int T = Cin. nextint ();  While (T! = 0 ){ -- T; Init (); solve ();}}  Static   Void  Prepare (){  Int I, J, K = 40 ; FAC [ 0] = FAC [1] = New Biginteger ("1" );  For (I = 2; I <= K; I ++) FAC [I] = FAC [I-1 ]. Multiply (biginteger. valueof (I ));  For (I = 0; I <= K; I ++ ) Isprime [I] = True  ; P = 0 ;  For (I = 2; I <= K; I ++ )  If  (Isprime [I]) {Prime [p ++] = I; For (J = I * I; j <= K; j + = I) isprime [I] = False  ;}}  Static   Void  Init (){  Int  I; n = 0 ;  For (I = 0; I <3; I ++ ) {A [I] = Cin. nextint (); n + =A [I];} divide (n );}  Static   Void Divide ( Int  N ){  Int  I; PN = 0 ;  For (I = 0; I <P & prime [I] * prime [I] <= N; I ++ )  If (N % prime [I] = 0 ) {P [pn ++] =Prime [I];  While (N % prime [I] = 0 ) N /= Prime [I];}  If (N> 1 ) P [pn ++] = N ;}  Static   Int Euler ( Int  N ){  Int I, ANS = N; For (I = 0; I <PN; I ++ )  If (N % P [I] = 0 ) Ans = ANS/P [I] * (p [I]-1 );  Return  Ans ;}  Static   Void  Solve () {ans = New Biginteger ("0" ); DFS ( 0, 1 , N ); If (N % 2 = 1 ){  For ( Int I = 0; I <3; I ++ ){  For ( Int J = 0; j <3; j ++ ) B [J] = A [J]; -- B [I];  If (B [I] <0 ) Continue  ; Ans = Ans. Add (calculate (2 ). Multiply (biginteger. valueof (N )));}}  Else  {  For ( Int I = 0; I <3; I ++ ) B [I] = A [I]; ans = Ans. Add (calculate (2). Multiply (biginteger. valueof (n/2 )));  For ( Int I = 0; I <3; I ++ )  For ( Int J = 0; j <3; j ++ ){  For ( Int K = 0; k <3; k ++ ) B [k] = A [k]; -- B [I]; -- B [J];  If (B [I] <0 | B [J] <0)  Continue  ; Ans = Ans. Add (calculate (2). Multiply (biginteger. valueof (n/2 );} Ans = Ans. Divide (biginteger. valueof (2 * N); system. Out. println (ANS );}  Static Biginteger calculate ( Int  M ){  Int I, n = 0 ; Biginteger ans = New Biginteger ("1");  For (I = 0; I <3; I ++ ){  If (B [I] % m! = 0 )  Return  Biginteger. Zero; B [I] /= M; n + = B [I];}  For (I = 0; I <3; I ++ ) {Ans = Ans. Multiply (comb (n, B [I]); n -=B [I];}  Return  Ans ;}  Static   Void DFS ( Int Cur, Int V, Int  X ){  Int I, CNT = 0, T = 1 ;  If (Cur = PN ){  For (I = 0; I <3; I ++) B [I] = A [I]; ans = Ans. Add (calculate (N/V). Multiply (biginteger. valueof (Euler (N/ V ))));  Return  ;}  While (X % P [cur] = 0 ){ ++ CNT; x /= P [cur];}  For (I = 0; I <= CNT; I ++ ) {DFS (cur + 1, V *T, x); t * = P [cur] ;}}  Static Biginteger comb ( Int N, Int  M ){  Return FAC [N]. Divide (FAC [m]). Divide (FAC [n- M]) ;}}