Division of the Kingdom

The Kingdom of Flatland is depicted as an infinite two-dimensional plane. Within this kingdom, there are (n) castles. To aid in map-making, a Cartesian coordinate system has been established. Each castle, specifically the (i)-th one, is positioned at the coordinates ((x_i + 0.5, y_i + 0.5)), where (x_i) and (y_i) are integers. All castle locations are unique.

In his later years, the king decided to divide the kingdom on the map among his sons using lines that run parallel to the coordinate axes. A line parallel to the (Ox) axis will have a (y) coordinate that is an integer for all points on the line; similarly, a line parallel to the (Oy) axis will have an (x) coordinate that is an integer. In both scenarios, these integer coordinates must not exceed (2 $\cdot$ 10^9) in absolute value. The king desires that each pair of castles be located in separate regions after the division.

Assist the king in dividing the kingdom using no more than (n−1) lines. Any two lines should intersect at most at one point.

Input

The first line contains an integer (n) ((1 $\le$ n $\le$ 100,000)) — the number of castles in the kingdom. The next (n) lines each contain two integers (x_i) and (y_i) ((-10^9 $\le$ x_i $\le$ 10^9), (-10^9 $\le$ y_i $\le$ 10^9)) — representing the integer parts of the coordinates of the castles.

Output

On the first line of the output, print the number of lines used. In the subsequent lines, print each line, one per line. If a line is parallel to the (Ox) axis, print the letter "(y)", followed by the (y) coordinate of all points on this line. Otherwise, print the letter "(x)", followed by the (x) coordinate of all points on this line.

Examples