Problem Statement

For real numbers $L$ and $R$, let us denote by $\[L,R)$ the set of real numbers greater than or equal to $L$ and less than $R$. Such a set is called a right half-open interval.

You are given $N$ right half-open intervals $\[L_i,R_i)$. Let $S$ be their union. Represent $S$ as a union of the minimum number of right half-open intervals.

Constraints

• $1 \\leq N \\leq 2\\times 10^5$
• $1 \\leq L_i \\lt R_i \\leq 2\\times 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $L_1$ $R_1$ $\\vdots$ $L_N$ $R_N$

Output

Let $k$ be the minimum number of right half-open intervals needed to represent $S$ as their union. Print $k$ lines containing such $k$ right half-open intervals $\[X_i,Y_i)$ in ascending order of $X_i$, as follows:

$X_1$ $Y_1$ $\\vdots$ $X_k$ $Y_k$

Sample Input 1

3
10 20
20 30
40 50

Sample Output 1

10 30
40 50

The union of the three right half-open intervals $\[10,20),\[20,30),\[40,50)$ equals the union of two right half-open intervals $\[10,30),\[40,50)$.

Sample Input 2

3
10 40
30 60
20 50

Sample Output 2

10 60

The union of the three right half-open intervals $\[10,40),\[30,60),\[20,50)$ equals the union of one right half-open interval $\[10,60)$.