{"problem":{"name":"Collision 2","description":{"content":"There are $N$ people in an $xy$\\-plane. Person $i$ is at $(X_i, Y_i)$. The positions of all people are different. We have a string $S$ of length $N$ consisting of `L` and `R`.   If $S_i =$ `R`, Person","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc243_c"},"statements":[{"statement_type":"Markdown","content":"There are $N$ people in an $xy$\\-plane. Person $i$ is at $(X_i, Y_i)$. The positions of all people are different.\nWe have a string $S$ of length $N$ consisting of `L` and `R`.  \nIf $S_i =$ `R`, Person $i$ is facing right; if $S_i =$ `L`, Person $i$ is facing left. All people simultaneously start walking in the direction they are facing. Here, right and left correspond to the positive and negative $x$\\-direction, respectively.\nFor example, the figure below shows the movement of people when $(X_1, Y_1) = (2, 3), (X_2, Y_2) = (1, 1), (X_3, Y_3) =(4, 1), S =$ `RRL`.\n![image](https://img.atcoder.jp/ghi/f33104f8bc05a920f2b74ead8ad1e3d2.png)\nWe say that there is a collision when two people walking in opposite directions come to the same position. Will there be a collision if all people continue walking indefinitely?\n\n## Constraints\n\n*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $0 \\leq X_i \\leq 10^9$\n*   $0 \\leq Y_i \\leq 10^9$\n*   $(X_i, Y_i) \\neq (X_j, Y_j)$ if $i \\neq j$.\n*   All $X_i$ and $Y_i$ are integers.\n*   $S$ is a string of length $N$ consisting of `L` and `R`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$X_1$ $Y_1$\n$X_2$ $Y_2$\n$\\vdots$\n$X_N$ $Y_N$\n$S$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc243_c","tags":[],"sample_group":[["3\n2 3\n1 1\n4 1\nRRL","Yes\n\nThis input corresponds to the example in the Problem Statement.  \nIf all people continue walking, Person $2$ and Person $3$ will collide. Thus, `Yes` should be printed."],["2\n1 1\n2 1\nRR","No\n\nSince Person $1$ and Person $2$ walk in the same direction, they never collide."],["10\n1 3\n1 4\n0 0\n0 2\n0 4\n3 1\n2 4\n4 2\n4 4\n3 3\nRLRRRLRLRR","Yes"]],"created_at":"2026-03-03 11:01:14"}}