static int countStrUtil ( int [ ] [ ] [ ] dp , int n , int bCount , int cCount ) {
  if ( bCount < 0 || cCount < 0 ) {
    return 0 ;
  }
  if ( n == 0 ) {
    return 1 ;
  }
  if ( bCount == 0 && cCount == 0 ) {
    return 1 ;
  }
  if ( dp [ n ] [ bCount ] [ cCount ] != - 1 ) {
    return dp [ n ] [ bCount ] [ cCount ] ;
  }
  int res = countStrUtil ( dp , n - 1 , bCount , cCount ) ;
  res += countStrUtil ( dp , n - 1 , bCount - 1 , cCount ) ;
  res += countStrUtil ( dp , n - 1 , bCount , cCount - 1 ) ;
  return ( dp [ n ] [ bCount ] [ cCount ] = res ) ;
}

static int countStrUtil ( int [ ] [ ] [ ] dp , int n , int bCount , int cCount ) { if ( bCount < 0 || cCount < 0 ) { return 0 ; } if ( n == 0 ) { return 1 ; } if ( bCount == 0 && cCount == 0 ) { return 1 ; } if ( dp [ n ] [ bCount ] [ cCount ] != - 1 ) { return dp [ n ] [ bCount ] [ cCount ] ; } int res = countStrUtil ( dp , n - 1 , bCount , cCount ) ; res += countStrUtil ( dp , n - 1 , bCount - 1 , cCount ) ; res += countStrUtil ( dp , n - 1 , bCount , cCount - 1 ) ; return ( dp [ n ] [ bCount ] [ cCount ] = res ) ; }
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