/*
Colectia personala de operatii pe numere mari - C++ ( classes )
Implementate de Robert Simoiu
Incluzand extragerea radacinii patrate cu un numar finit de zecimale
*/
# include <cmath>
# include <cstdio>
# include <cstring>
# include <vector>
using namespace std ;
/*
precizare :
1. Daca vreti sa faceti a = b + c, in loc de a += b , trebuie pus in loc de void operator += ( ... )
Mare operator + ( ... ) , si sa returnati un vector Mare ( exemplu prima functie, Mare operator + ( Mare& ) )
2. Base inseamna baza si nbase numarul maxim de cifre al unui numar din baza base
*/
# define MAX 100 // * nbase = numarul de cifre
# define verf( X, i ) ( i <= X[0] ? X[i] : 0 )
# define A ( *this )
class Mare : protected vector < int > {
static const int base = 1000000000, nbase = 9 ;
public :
Mare ( ) ;
Mare ( int ) ;
void operator = ( char* ) ;
void operator += ( Mare& ) ;
void operator *= ( int ) ;
void operator *= ( Mare& ) ;
void operator -= ( Mare& ) ;
void operator <<= ( int ) ;
void operator >>= ( int ) ;
void operator /= ( int ) ;
void operator /= ( Mare& ) ;
void operator %= ( int ) ;
void operator %= ( Mare& ) ;
void operator ++ ( void ) ;
void operator ++ ( int ) ;
void operator -- ( void ) ;
void operator -- ( int ) ;
Mare operator + ( Mare& ) ;
int zero ( void ) ;
int comparare ( Mare& ) ;
bool operator < ( Mare& ) ;
bool operator <= ( Mare& ) ;
bool operator > ( Mare& ) ;
bool operator >= ( Mare& ) ;
bool operator == ( Mare& ) ;
bool operator != ( Mare& ) ;
void operator |= ( Mare& ) ;
void operator &= ( Mare& ) ;
void operator ^= ( Mare& ) ;
void afis ( void ) ;
void afis_rad ( int ) ;
void obtain ( int, int* ) ;
void pow ( int ) ;
void radical_cb ( Mare& ) ;
void radical_normal ( Mare&, int ) ;
void transform_2 ( int* ) ;
void transform_10 ( int* ) ;
void transform_210 ( int* ) ;
} ;
Mare :: Mare () { // A = 0
this -> resize ( MAX ) ;
}
Mare :: Mare ( int X ) { // A = X
this -> resize ( MAX ) ;
for ( A[0] = 0; X ; X /= base ) {
A[ ++A[0] ] = X % base ;
}
}
void Mare :: operator = ( char *X ) { // A = X ( sir )
A[0] = 0;
if ( X ) {
for ( int h = strlen ( X ) ; h > 0 ; h -= nbase ) {
++A[0] ;
for ( int i = max ( 0, h - nbase ) ; i < h; ++i ) {
A[ A[0] ] = A[ A[0] ] * 10 + X[i] - '0' ;
}
}
}
}
void Mare :: operator += ( Mare &B ) { // A += B
int i, t = 0;
for ( i = 1; i <= A[0] || i <= B[0] || t; ++i, t /= base )
A[i] = ( t += verf ( A, i ) + verf ( B, i ) ) % base ;
A[0] = i - 1;
}
void Mare :: operator *= ( int B ) { // A *= B
int i = 1;
for ( long long t = 0; i <= A[0] || t; ++i, t /= base )
A[i] = ( t += 1LL * verf ( A, i ) * B ) % base ;
A[0] = i - 1;
}
void Mare :: operator *= ( Mare &B ) { // A *= B
Mare C ;
for ( int i = 1, j; i <= A[0]; ++i ) {
long long t = 0 ;
for ( j = 1; j <= B[0] || t; ++j, t /= base)
C[i + j - 1] = ( t += C[i + j - 1] + 1LL * verf ( A, i ) * verf ( B, j ) ) % base;
if ( i + j - 2 > C[0] )
C[0] = i + j - 2;
}
A = C ;
}
void Mare :: operator -= ( Mare &B ) { // A -= B, ∀ A ≥ B
int t = 0;
for ( int i = 1; i <= A[0]; ++i ) {
t = ( A[i] -= verf ( B, i ) + t ) < 0 ;
A[i] += t * base ;
}
for ( ; A[0] > 1 && !A[A[0]]; --A[0] ) ;
}
void Mare :: operator <<= ( int Count ) { // A *= 10^Count
if ( Count ) {
if ( A.zero () ) A = 1 ;
Mare sol = 10 ;
sol.pow ( Count ), A *= sol ;
}
}
void Mare :: operator >>= ( int Count ) { // A /= 10^Count
if ( Count ) {
Mare sol = 10 ;
sol.pow ( Count ), A /= sol ;
}
}
void Mare :: operator /= ( int B ) { // A /= B
long long t = 0;
for ( int i = A[0]; i > 0; i--, t %= B )
A[i] = ( t = 1LL * t * base + A[i] ) / B ;
for ( ; A[0] > 1 && !A[ A[0] ]; --A[0] ) ;
}
# define ck ( i / nbase + ( i % nbase != 0 ) )
void Mare :: operator /= ( Mare &B ) { // A /= B
int X[MAX * nbase];
Mare R = 0, T ;
A.transform_10 ( X ) ;
fill_n ( A.begin () + 1, A[0], 0 ) ;
for ( int i = X[0]; i ; --i ) {
R *= R.zero () ? 0 : 10, T = X[i], R += T ;
for ( A[ ck ] *= 10; B <= R ; ++A[ ck ], R -= B ) ;
}
for ( ; !A[ A[0] ] && A[0] > 1 ; --A[0] ) ;
}
void Mare :: operator %= ( int B ) { // A %= B
long long t = 0;
for ( int i = A[0]; i ; --i )
t = ( 1LL * t * base + A[i] ) % B ;
A = t ;
}
void Mare :: operator %= ( Mare &B ) { // A %= B
int X[MAX * nbase] ; Mare R = 0, T, C ;
A.transform_10 ( X ) ;
fill_n ( C.begin () + 1, A[0], 0 ) ;
for ( int i = X[0]; i ; --i ) {
R *= R.zero () ? 0 : 10, T = X[i], R += T ;
for ( C[ ck ] *= 10; B <= R ; ++C[ ck ], R -= B ) ;
}
A = R ;
}
# undef ck
void Mare :: operator ++ ( void ) { // ++A
Mare B = 1 ;
A += B ;
}
void Mare :: operator ++ ( int ) { // A++
++A ;
}
void Mare :: operator -- ( void ) { // --A
Mare B = 1 ;
A -= B ;
}
void Mare :: operator -- ( int ) { // A--
--A ;
}
Mare Mare :: operator + ( Mare &B ) { // C = A + B
int i, t = 0; Mare C ;
for ( i = 1; i <= A[0] || i <= B[0] || t; ++i, t /= base )
C[i] = ( t += verf ( A, i ) + verf ( B, i ) ) % base ;
C[0] = i - 1;
return C ;
}
int Mare :: zero ( void ) { // A == 0 ?
return A[0] == 0 || A[0] == 1 && A[1] == 0 ;
}
int Mare :: comparare ( Mare &B ) {
for ( ; A[0] && !A[A[0]] ; --A[0] ) ;
for ( ; B[0] && !B[B[0]] ; --B[0] ) ;
if ( A[0] < B[0] ) return -1;
else if ( A[0] > B[0] ) return 1;
for ( int i = A[0]; i > 0; --i )
if ( A[i] < B[i] ) return -1;
else if ( A[i] > B[i] ) return 1;
return 0;
}
bool Mare :: operator < ( Mare &B ) { // A < B ?
return A.comparare ( B ) == -1 ;
}
bool Mare :: operator <= ( Mare &B ) { // A <= B ?
return A.comparare ( B ) != 1 ;
}
bool Mare :: operator > ( Mare &B ) { // A > B ?
return A.comparare ( B ) == 1 ;
}
bool Mare :: operator >= ( Mare &B ) {// A >= B ?
return A.comparare ( B ) != -1 ;
}
bool Mare :: operator == ( Mare &B ) {// A == B ?
return A.comparare ( B ) == 0 ;
}
bool Mare :: operator != ( Mare &B ) {// A != B ?
return A.comparare ( B ) != 0 ;
}
void Mare :: operator |= ( Mare &B ) { // A |= B
int X[MAX * nbase], Y[MAX * nbase] ;
A.transform_2 ( X ) , B.transform_2 ( Y ) ;
for ( int i = 1; i <= X[0] && i <= Y[0]; ++i )
X[i] |= Y[i] ;
if ( X[0] < Y[0] ) {
for ( int i = X[0] + 1 ; i <= Y[0] ; ++i )
X[i] = Y[i] ;
X[0] = Y[0] ;
}
A.transform_210 ( X ) ;
}
void Mare :: operator &= ( Mare &B ) { // A &= B
int X[MAX * nbase], Y[MAX * nbase] ;
A.transform_2 ( X ) , B.transform_2 ( Y ) ;
for ( int i = 1; i <= X[0] && i <= Y[0]; ++i )
X[i] &= Y[i] ;
X[0] = min ( X[0], Y[0] ) ;
A.transform_210 ( X ) ;
}
void Mare :: operator ^= ( Mare &B ) { // A ^= B
int X[MAX * nbase], Y[MAX * nbase] ;
A.transform_2 ( X ) , B.transform_2 ( Y ) ;
for ( int i = 1; i <= X[0] && i <= Y[0]; ++i )
X[i] ^= Y[i] ;
if ( X[0] < Y[0] ) {
for ( int i = X[0] + 1 ; i <= Y[0] ; ++i )
X[i] = Y[i] ;
X[0] = Y[0] ;
}
A.transform_210 ( X ) ;
}
void Mare :: radical_cb ( Mare &B ) { // B = sqrt ( A ) ; doar parte intreaga
Mare cnt, X ;
for ( cnt = 1; cnt < A; cnt *= 2 ) ;
for ( B[0] = 1 ; ! cnt.zero () ; cnt /= 2 ) {
X = cnt, X += B, X *= X ;
if ( X <= A )
B += cnt ;
}
}
void Mare :: afis ( void ) { // afisarea
printf ( "%d", A[ A[0] ] ) ;
for ( int i = A[0] - 1; i ; --i ) {
printf ( "%09d", A[i] ) ;
}
}
void Mare :: afis_rad ( int nrzecimale ) { // afisarea radicalului
int X[MAX * nbase] ;
A.transform_10 ( X ) ;
for ( int i = X[0]; i > nrzecimale ; --i )
printf ( "%d", X[i] ) ;
printf ( "." ) ;
for ( int i = nrzecimale ; i ; --i ) {
printf ( "%d", X[i] ) ;
}
}
void Mare :: obtain ( int x, int *X ) {
int S[10] = { 0 } ;
for ( int i = A[x]; i ; i /= 10 )
S[ ++S[0] ] = i % 10 ;
for ( int i = 1; i <= S[0] ; ++i )
X[ ++X[0] ] = S[i] ;
if ( x != A[0] )
for ( int i = S[0]; i < nbase; ++i )
X[ ++X[0] ] = 0 ;
}
void Mare :: pow ( int P ) { // A = A^P
Mare B = 1 ;
for ( ; P ; P >>= 1 ) {
if ( P & 1 )
B *= A ;
A *= A ;
}
A = B ;
}
void Mare :: transform_2 ( int *X ) { // baza 'base' -> baza 2
Mare B = A ;
X[0] = 0 ;
for ( ; !B.zero () ; X[ ++X[0] ] = B[ 1 ] & 1, B /= 2 ) ;
}
void Mare :: transform_10 ( int *X ) { // baza 'base' -> baza 10
X[0] = 0 ;
for ( int i = 1; i <= A[0]; ++i )
obtain ( i, X ) ;
}
void Mare :: transform_210 ( int *X ) { // baza 2 -> baza 'base'
Mare B = 1 ; A = 0 ;
for ( int i = 1; i <= X[0]; ++i, B *= 2 ) {
if ( X[i] == 1 ) A += B ;
}
}
void Mare :: radical_normal ( Mare &B, int nrzecimale ) {
int AUX = 0, i , j = 0 ; int X[MAX * nbase] ;
Mare C, D, E, F, U = 9 , Z = 1 ;
A.transform_10 ( X ), i = X[0] ;
X[0] & 1 ? AUX = X[i--] : ( AUX = X[i--], AUX *= 10, AUX += X[i--] ) ;
int aux = static_cast < int > ( sqrt ( AUX ) ) ;
B = aux ;
if ( X[0] > 2 ) {
AUX -= aux * aux;
E = AUX, E <<= 1, F = X[i--] ;
if ( AUX ) E += F, E <<= 1 ;
else E = F ;
if ( AUX == 0 && X[i + 1] ) E <<= 1 ;
F = X[i--], E += F, C = E, F = B, F *= 2, E = F ;
D = C, D >>= 1, D /= E, U < D ? D = 9 : 0 ;
E <<= 1, E += D, E *= D ;
while ( C < E )
D -= Z, F = B, F *= 2, E = F, E <<= 1, E += D, E *= D ;
C -= E, B <<= 1, B += D ;
} else {
C = AUX - ( aux * aux ) ;
}
if ( !C.zero () || i > 0 ) {
for ( i = i; i > 0 || j < nrzecimale ; ) {
if ( i > 0 ) {
E = X[i--], F = 0, F <<= 1, F = E, E = X[i--];
if ( X[i + 2] ) F <<= 1, F += E ;
else F = E ;
} else {
++j, F = 0 ;
if ( j == 1 && C.zero () ) {
for ( int i = 1; i <= nrzecimale ; ++i )
B <<= 1 ;
return ;
}
}
if ( !C.zero () || i == 3 + ( X[0] % 2 == 0 ) && AUX ) {
C <<= 2, C += F ;
} else {
C = F ;
}
F = B, F *= 2, E = F ;
D = C, D >>= 1, D /= E, U < D ? D = 9 : 0 ;
E <<= 1, E += D, E *= D ;
while ( C < E )
D -= Z, F = B, F *= 2, E = F, E <<= 1, E += D, E *= D ;
C -= E, B <<= 1, B += D ;
}
} else {
for ( int i = 1; i <= nrzecimale ; ++i )
B <<= 1 ;
}
}
# undef A
#define Smerenie 1000
int N;
Mare d[2][Smerenie + 1];
int gcd[Smerenie + 1][Smerenie + 1];
/** gcd(a, b). **/
int cmmdc(int a, int b) {
return b ? cmmdc(b, a % b) : a;
}
/** Precalculeaza gcd-urile. **/
void init() {
int i, j;
for (i = 1; i <= Smerenie; i++) {
for (j = i; j <= Smerenie; j++) {
gcd[i][j] = gcd[j][i] = cmmdc(i, j);
}
}
}
int main ( void ) {
int i, j, val, side = 0, write;
FILE *f = fopen("indep.in", "r");
init();
/* Citirea datelor. */
fscanf(f, "%d", &N);
for (i = 1; i <= N; i++) {
fscanf(f, "%d", &val);
/* Programare dinamica pe 2 linii. */
write = (i & 1);
for (j = 1; j <= Smerenie; j++) {
d[write][j] = d[side][j];
}
for (j = 1; j <= Smerenie; j++) {
d[write][gcd[val][j]] += d[write][j];
}
++d[side = write][val];
}
fclose(f);
/* Afisarea solutiei. */
freopen("indep.out", "w", stdout);
d[side][1].afis();
fclose(stdout);
/// Multumim Doamne!
puts("Doamne ajuta!");
}