CF566B Replicating Processes

A Large Software Company develops its own social network. Analysts have found that during the holidays, major sporting events and other significant events users begin to enter the network more frequently, resulting in great load increase on the infrastructure. As part of this task, we assume that the social network is $ 4n $ processes running on the $ n $ servers. All servers are absolutely identical machines, each of which has a volume of RAM of $ 1 $ GB = $ 1024 $ MB $ ^{(1)} $ . Each process takes 100 MB of RAM on the server. At the same time, the needs of maintaining the viability of the server takes about $ 100 $ more megabytes of RAM. Thus, each server may have up to $ 9 $ different processes of social network. Now each of the $ n $ servers is running exactly $ 4 $ processes. However, at the moment of peak load it is sometimes necessary to replicate the existing $ 4n $ processes by creating $ 8n $ new processes instead of the old ones. More formally, there is a set of replication rules, the $ i $ -th ( $ 1

The first line of the input contains integer $ n $ ( $ 1

If the required order of performing rules does not exist, print "NO" (without the quotes). Otherwise, print in the first line "YES" (without the quotes), and in the second line — a sequence of $ 4n $ numbers from $ 1 $ to $ 4n $ , giving the numbers of the rules in the order they are applied. The sequence should be a permutation, that is, include each number from $ 1 $ to $ 4n $ exactly once. If there are multiple possible variants, you are allowed to print any of them.

$ ^{(1)} $ To be extremely accurate, we should note that the amount of server memory is $ 1 $ GiB = $ 1024 $ MiB and processes require $ 100 $ MiB RAM where a gibibyte (GiB) is the amount of RAM of $ 2^{30} $ bytes and a mebibyte (MiB) is the amount of RAM of $ 2^{20} $ bytes. In the first sample test the network uses two servers, each of which initially has four launched processes. In accordance with the rules of replication, each of the processes must be destroyed and twice run on another server. One of the possible answers is given in the statement: after applying rules $ 1 $ and $ 2 $ the first server will have $ 2 $ old running processes, and the second server will have $ 8 $ ( $ 4 $ old and $ 4 $ new) processes. After we apply rules $ 5 $ and $ 6 $ , both servers will have $ 6 $ running processes ( $ 2 $ old and $ 4 $ new). After we apply rules $ 3 $ and $ 7 $ , both servers will have $ 7 $ running processes ( $ 1 $ old and $ 6 $ new), and after we apply rules $ 4 $ and $ 8 $ , each server will have $ 8 $ running processes. At no time the number of processes on a single server exceeds $ 9 $ . In the second sample test the network uses three servers. On each server, three processes are replicated into two processes on the same server, and the fourth one is replicated in one process for each of the two remaining servers. As a result of applying rules $ 2,3,4,6,7,8,10,11,12 $ each server would have $ 7 $ processes ( $ 6 $ old and $ 1 $ new), as a result of applying rules $ 1,5,9 $ each server will have $ 8 $ processes. At no time the number of processes on a single server exceeds $ 9 $ .