9825번 - MODSUM 다국어

In this task, you are given the following function \(f\) with \(n\) parameters:

\[f(x_1, \dots, x_n) = \left(\left(\left(x_1 + x_2 + \dots + x_n\right)^4 + 2 \times \left(x_1 + x_2 + \dots + x_n \right)^2 \right) \mod {5} \right) + 1\]

As arguments, \(f\) accepts only integer values. Your task is to compute the sum of all values of \(f\), where each input \(x_i\) ranges from an integer value \(v_i\) to \(w_i\). In other words, you need to compute

\[\sum_{x_1 = v_1}^{w_1}\sum_{x_2 = v_2}^{w_2} \cdots \sum_{x_n = v_n}^{w_1} f(x_1, \dots, x_n)\]

For example, if \(n = 3, v_1 = 2, w_1 = 3, v_2 = 10, w_2 = 12, v_3 = 17\) and \(w_3 = 17\), then the result should be 19, since \(f(2, 10, 17) = 4, f(2, 11, 17) = 1, f(2, 12, 17) = 4, f(3, 10, 17) = 1, f(3, 11, 17) = 4\) and \(f(3, 12, 17) = 5\).

Important note: You can assume that the result will always be less than 1,000,000.

Your program must read from the standard input. The input consists of \(n\), where \(1 \le n \le 1000\), followed by \(n\) pairs of numbers, \(v_i\) and \(w_i\), each of which ranges from 0 to 100. For each pair \(v_i\) and \(w_i\), you can assume that \(v_i \le w_i\).

Your program must write to the standard output the required sum.