Tinted Glass Window

문제

You are laying N rectangular pieces of grey-tinted glass to make a stained glass window. Each piece of glass adds an integer value “tint-factor”. Where two pieces of glass overlap, the tint-factor is the sum of their tint-factors.

You know the desired position for each piece of glass and these pieces of glass are placed such that the sides of each rectangle are parallel to either the x-axis or the y-axis (that is, there are no “diagonal” pieces of glass).

You would like to know the total area of the finished stained glass window with a tint-factor of at least T.

입력

The first line of input is the integer N (1 ≤ N ≤ 1000), the number of pieces of glass. The second line of input is the integer T (1 ≤ T ≤ 1 000 000 000), the threshold for the tint-factor. Each of the next N lines contain five integers, representing the position of the top-left and bottom-right corners of the ith piece of tinted glass followed by the tint-factor of that piece of glass. Specifically, the integers are placed in the order x_l y_t x_r y_b t_i, where the top-left corner is at (x_l, y_t) and the bottom-right corner is at (x_r, y_b), and tint-factor is t_i. You can assume that 1 ≤ t_i ≤ 1 000 000. The top-most, left-most co-ordinate where glass can be placed is (0, 0) and you may assume 0 ≤ x_l < x_r ≤ K and 0 < y_t < y_b ≤ K, N ≤ 1000 and K ≤ 1 000 000 000.

출력

Output the total area of the finished stained glass window which has a tint-factor of at least T. All output will be less than 2⁶⁴, and the output for some test cases will be larger than 2³².