static int countStaircases ( int N ) {
  int [ ] [ ] memo = new int [ N + 5 ] [ N + 5 ] ;
  for ( int i = 0 ;
  i <= N ;
  i ++ ) {
    for ( int j = 0 ;
    j <= N ;
    j ++ ) {
      memo [ i ] [ j ] = 0 ;
    }
  }
  memo [ 3 ] [ 2 ] = memo [ 4 ] [ 2 ] = 1 ;
  for ( int i = 5 ;
  i <= N ;
  i ++ ) {
    for ( int j = 2 ;
    j <= i ;
    j ++ ) {
      if ( j == 2 ) {
        memo [ i ] [ j ] = memo [ i - j ] [ j ] + 1 ;
      }
      else {
        memo [ i ] [ j ] = memo [ i - j ] [ j ] + memo [ i - j ] [ j - 1 ] ;
      }
    }
  }
  int answer = 0 ;
  for ( int i = 1 ;
  i <= N ;
  i ++ ) answer = answer + memo [ N ] [ i ] ;
  return answer ;
}

static int countStaircases ( int N ) { int [ ] [ ] memo = new int [ N + 5 ] [ N + 5 ] ; for ( int i = 0 ; i <= N ; i ++ ) { for ( int j = 0 ; j <= N ; j ++ ) { memo [ i ] [ j ] = 0 ; } } memo [ 3 ] [ 2 ] = memo [ 4 ] [ 2 ] = 1 ; for ( int i = 5 ; i <= N ; i ++ ) { for ( int j = 2 ; j <= i ; j ++ ) { if ( j == 2 ) { memo [ i ] [ j ] = memo [ i - j ] [ j ] + 1 ; } else { memo [ i ] [ j ] = memo [ i - j ] [ j ] + memo [ i - j ] [ j - 1 ] ; } } } int answer = 0 ; for ( int i = 1 ; i <= N ; i ++ ) answer = answer + memo [ N ] [ i ] ; return answer ; }
(method_declaration (modifiers) type: (integral_type) name: (identifier) parameters: (formal_parameters (formal_parameter type: (integral_type) name: (identifier))) body: (block (local_variable_declaration type: (array_type element: (integral_type) dimensions: (dimensions)) declarator: (variable_declarator name: (identifier) value: (array_creation_expression type: (integral_type) dimensions: (dimensions_expr (binary_expression left: (identifier) right: (decimal_integer_literal))) dimensions: (dimensions_expr (binary_expression left: (identifier) right: (decimal_integer_literal)))))) (for_statement init: (local_variable_declaration type: (integral_type) declarator: (variable_declarator name: (identifier) value: (decimal_integer_literal))) condition: (binary_expression left: (identifier) right: (identifier)) update: (update_expression (identifier)) body: (block (for_statement init: (local_variable_declaration type: (integral_type) declarator: (variable_declarator name: (identifier) value: (decimal_integer_literal))) condition: (binary_expression left: (identifier) right: (identifier)) update: (update_expression (identifier)) body: (block (expression_statement (assignment_expression left: (array_access array: (array_access array: (identifier) index: (identifier)) index: (identifier)) right: (decimal_integer_literal))))))) (expression_statement (assignment_expression left: (array_access array: (array_access array: (identifier) index: (decimal_integer_literal)) index: (decimal_integer_literal)) right: (assignment_expression left: (array_access array: (array_access array: (identifier) index: (decimal_integer_literal)) index: (decimal_integer_literal)) right: (decimal_integer_literal)))) (for_statement init: (local_variable_declaration type: (integral_type) declarator: (variable_declarator name: (identifier) value: (decimal_integer_literal))) condition: (binary_expression left: (identifier) right: (identifier)) update: (update_expression (identifier)) body: (block (for_statement init: (local_variable_declaration type: (integral_type) declarator: (variable_declarator name: (identifier) value: (decimal_integer_literal))) condition: (binary_expression left: (identifier) right: (identifier)) update: (update_expression (identifier)) body: (block (if_statement condition: (parenthesized_expression (binary_expression left: (identifier) right: (decimal_integer_literal))) consequence: (block (expression_statement (assignment_expression left: (array_access array: (array_access array: (identifier) index: (identifier)) index: (identifier)) right: (binary_expression left: (array_access array: (array_access array: (identifier) index: (binary_expression left: (identifier) right: (identifier))) index: (identifier)) right: (decimal_integer_literal))))) alternative: (block (expression_statement (assignment_expression left: (array_access array: (array_access array: (identifier) index: (identifier)) index: (identifier)) right: (binary_expression left: (array_access array: (array_access array: (identifier) index: (binary_expression left: (identifier) right: (identifier))) index: (identifier)) right: (array_access array: (array_access array: (identifier) index: (binary_expression left: (identifier) right: (identifier))) index: (binary_expression left: (identifier) right: (decimal_integer_literal)))))))))))) (local_variable_declaration type: (integral_type) declarator: (variable_declarator name: (identifier) value: (decimal_integer_literal))) (for_statement init: (local_variable_declaration type: (integral_type) declarator: (variable_declarator name: (identifier) value: (decimal_integer_literal))) condition: (binary_expression left: (identifier) right: (identifier)) update: (update_expression (identifier)) body: (expression_statement (assignment_expression left: (identifier) right: (binary_expression left: (identifier) right: (array_access array: (array_access array: (identifier) index: (identifier)) index: (identifier)))))) (return_statement (identifier))))