Winding polygonal line

Vasya has $$$n$$$ different points $$$A_1, A_2, \ldots A_n$$$ on the plane. No three of them lie on the same line He wants to place them in some order $$$A_{p_1}, A_{p_2}, \ldots, A_{p_n}$$$, where $$$p_1, p_2, \ldots, p_n$$$ — some permutation of integers from $$$1$$$ to $$$n$$$.

After doing so, he will draw oriented polygonal line on these points, drawing oriented segments from each point to the next in the chosen order. So, for all $$$1 \leq i \leq n-1$$$ he will draw oriented segment from point $$$A_{p_i}$$$ to point $$$A_{p_{i+1}}$$$. He wants to make this polygonal line satisfying $$$2$$$ conditions:

• it will be non-self-intersecting, so any $$$2$$$ segments which are not neighbors don't have common points.
• it will be winding.

Vasya has a string $$$s$$$, consisting of $$$(n-2)$$$ symbols "L" or "R". Let's call an oriented polygonal line winding, if its $$$i$$$-th turn left, if $$$s_i = $$$ "L" and right, if $$$s_i = $$$ "R". More formally: $$$i$$$-th turn will be in point $$$A_{p_{i+1}}$$$, where oriented segment from point $$$A_{p_i}$$$ to point $$$A_{p_{i+1}}$$$ changes to oriented segment from point $$$A_{p_{i+1}}$$$ to point $$$A_{p_{i+2}}$$$. Let's define vectors $$$\overrightarrow{v_1} = \overrightarrow{A_{p_i} A_{p_{i+1}}}$$$ and $$$\overrightarrow{v_2} = \overrightarrow{A_{p_{i+1}} A_{p_{i+2}}}$$$. Then if in order to rotate the vector $$$\overrightarrow{v_1}$$$ by the smallest possible angle, so that its direction coincides with the direction of the vector $$$\overrightarrow{v_2}$$$ we need to make a turn counterclockwise, then we say that $$$i$$$-th turn is to the left, and otherwise to the right. For better understanding look at this pictures with some examples of turns:

There are left turns on this picture

There are right turns on this picture

You are given coordinates of the points $$$A_1, A_2, \ldots A_n$$$ on the plane and string $$$s$$$. Find a permutation $$$p_1, p_2, \ldots, p_n$$$ of the integers from $$$1$$$ to $$$n$$$, such that the polygonal line, drawn by Vasya satisfy two necessary conditions.