Vadim is a big fan of piecewise linear functions. They have their limitations, and not every function can be represented as piecewise linear. Vadim will gladly tell you what they are.

A function is called piecewise linear if its graph can be represented as a polyline with N vertices. Specifically, it is defined by n pairs of numbers (x₁, y₁), (x₂, y₂), …, (x_N, y_N), which are the coordinates of the vertices of the polyline. The condition must hold that x₁ < x₂ < x₃ < … < x_N.

This set of points defines a function of one argument, whose value at x_i is y_i, and on the intervals between these points, it is linear. The domain of such a function is the segment [x₁, x_N].

Valya invented his own class of functions with one variable, which he called modular. A modular function consists of N terms, each of which has one of two forms: |a_i · x + b_i| or −|a_i · x + b_i|. Here, x is the variable, and a_i and b_i are the parameters of the function, while | … | denotes the absolute value. Thus, a modular function with N terms has the form ± |a₁ x + b₁| ± |a₂ x + b₂| ± … ± |a_N x + b_N|.

Vadim wanted to check whether modular functions are not worse than his favorite piecewise linear ones. He brought a piecewise linear function with N vertices. Now try to find a modular function with exactly N terms that is identically equal to the given piecewise linear function on the segment [x₁, x_N].

The first line contains an integer N — the number of vertices of the polyline (2 ≤ N ≤ 10⁵).

Next, there are n lines, each containing two integers x_i, y_i — the coordinates of the next vertex (−10⁵ ≤ x_i, y_i ≤ 10⁵).

It is guaranteed that the coordinates x_i are strictly increasing, that is, x₁ < x₂ < x₃ < … < x_N.

Output a single line containing the modular function with exactly N terms that is identically equal to the given piecewise linear function on the segment [x₁, x_N]. Follow the format shown in the examples.

The function should consist of N terms |a_i x + b_i|, separated by the signs + and - (codes 43 and 45). It is allowed to place a leading minus before the first term. Each term must be enclosed in two symbols | (code 124). Inside the term, there must be a sign + (or -, if b_i is negative). The left operand consists of a real number a_i and the variable x (code 120); the multiplication sign between them does not need to be written, it is implied. It is not allowed to omit a_i or b_i, even if a_i = 1 or b_i = 0; the left operand cannot be omitted if a_i = 0.

There must be exactly N such terms. It is allowed to use terms that are identically equal to zero. They can be written as |0x+0|.

The size of the output file must not exceed 8 MB. The answer is considered correct if at any point in the segment [x₁, x_N], the value of your modular function differs from the value of the given piecewise linear function by no more than 0.01.

Illustration for the third example: