Birthday

Sang-geun received N intervals as a birthday gift. Each interval is a numeric interval written as [A, B], where A and B are integers.

He wants to build the longest possible sequence from the intervals he has. All intervals in the sequence must be distinct, and each interval must contain the interval immediately after it. Interval [A, B] contains interval [C, D] when A ≤ C and D ≤ B.

Find one longest interval sequence that satisfies these conditions.

The first line contains the number of intervals N. (1 ≤ N ≤ 100,000)

Each of the next N lines contains two integers A and B describing an interval [A, B]. (1 ≤ A < B ≤ 1,000,000)

Print K, the length of the sequence, on the first line. Then print K lines containing the intervals in sequence order. Each interval must be printed in the same format as the input: A B.