You are given $n$ intervals and their starts are all unique and also their ends are all unique. No two intervals may include each other (means there are no two different intervals $[l, r]$ and $[L, R]$ which $l \leq L < R \le r$).
Count the number of subsets of intervals in which their union is as same as all $n$ intervals union modulo $10^9+7$.
Formally, consider the interval's set $A$ and count the number $B \subseteq A$ which $\cup_{i \in A} i = \cup_{i \in B} i$ modulo $10^9+7$.

The union of two intervals $[l, r]$ and $[L, R]$ displayed as $[l, r] \cup [L, R]$ is $\{ x\in\mathbb{R} \ | \ l \le x \le r \ \mbox{or} \ L \le x \le R \}$.

Input format

• The first line contains only an integer $n$ denoting the number of intervals.
• Next $n$ lines contain two space-separated integers $l_i$ and $r_i$ ($l_i < r_i$) the interval is $[l_i, r_i]$.

  $1 \leq n \leq 3 \times 10^5$

  $1 \leq l_i < r_i \leq 10^9$

  It is guaranteed all $l_i$s are unique and also all $r_i$s are unique. No two intervals may include each other.

Output format

The output contains an integer denoting the number of subsets with provided conditions modulo $10^9+7$.