static int minimumChanges ( int arr [ ] , int n , int d ) {
  int maxFreq = - 1 ;
  HashMap < Integer , Integer > freq = new HashMap < Integer , Integer > ( ) ;
  for ( int i = 0 ;
  i < n ;
  ++ i ) {
    int a0 = arr [ i ] - ( i ) * d ;
    if ( freq . containsKey ( a0 ) ) {
      freq . put ( a0 , freq . get ( a0 ) + 1 ) ;
    }
    else freq . put ( a0 , 1 ) ;
    if ( freq . get ( a0 ) > maxFreq ) maxFreq = freq . get ( a0 ) ;
  }
  return ( n - maxFreq ) ;
}

static int minimumChanges ( int arr [ ] , int n , int d ) { int maxFreq = - 1 ; HashMap < Integer , Integer > freq = new HashMap < Integer , Integer > ( ) ; for ( int i = 0 ; i < n ; ++ i ) { int a0 = arr [ i ] - ( i ) * d ; if ( freq . containsKey ( a0 ) ) { freq . put ( a0 , freq . get ( a0 ) + 1 ) ; } else freq . put ( a0 , 1 ) ; if ( freq . get ( a0 ) > maxFreq ) maxFreq = freq . get ( a0 ) ; } return ( n - maxFreq ) ; }
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