给定一个整数多重集 $S = \{x_1, x_2, \dots, x_n\}$，其中 $x_i = 2^{a_i} \cdot 3^{b_i}$。
考虑 $S$ 的所有 $2^n - 1$ 个非空子集。对于每个子集，求其最小公倍数（LCM），并输出这些值的总和。由于答案可能非常大，请输出总和对 $10^9 + 7$ 取模的结果。
第一行包含一个整数 $n$ ($1 \le n \le 10^5$)。接下来 $n$ 行，每行包含两个整数 $a_i, b_i$ ($0 \le a_i, b_i \le 10^9$)。
输出一个整数，即问题的答案。
2 0 1 1 0
11
3 1 2 2 1 1 2
174
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