Connection Status:
Competition Arena > RPSRobots

RPSRobots

2016 TCO Algo 3B · 2016-03-24 · by cgy4ever

2016 TCO Algo 3B · 2016-03-24 · by cgy4ever · Advanced Math
Class Name: RPSRobots
Return Type: int
Method Name: countGoodSet
Arg Types: (int, vector<string>, int, int, int, int)
Problem Statement

Problem Statement

This task references the traditional game Rock-Paper-Scissors. In this game each of the two players simultaneously chooses one of those three objects. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. If both players choose the same object, the game is a tie.


We have n Rock-Paper-Scissors robots. Each robot has a fixed string called strategy and a nonnegative integer called state. Each character in the robot's strategy is one of 'R', 'P', and 'S', denoting Rock, Paper, and Scissors, respectively. The strategies of all robots have the same length: k.


Whenever a robot plays one round of Rock-Paper-Scissors, he performs the following steps:
  1. Use strategy[state modulo k] as his choice in the round of the game.
  2. Increment state by 1.

For example, if strategy = "RRS" and state = 10, then the next few moves will be: Rock, Scissors, Rock, Rock, Scissors, Rock, Rock, Scissors ... A match between two robots consists of exactly k consecutive rounds. The result of the match is the pair (number of rounds won by the first robot, number of rounds won by the second robot). Sometimes the result will depend on the initial states of both robots, and in other cases the result will be same regardless of their states. A pair of robots is called attuned if the result of their match is independent from their states.


For example, if two robots have strategies "RPS" and "RSP", the result of their match will be (1,1), regardless of their states at the beginning of the match. Hence, this pair of robots is attuned. On the other hand, consider two robots with strategies "RPS" and "RPS". The result of this match can be (0,0), (3,0), or (0,3) based on the robots' initial states. Hence, this second pair of robots is not attuned.


You are given a set of robots in a format that is described below. A non-empty subset of these robots is called attuned if all pairs of robots in the subset are attuned. (Note that trivially all subsets of size 1 are attuned as well.) Please compute and return the number of attuned subsets of robots, modulo 10^9 + 7.


You are given the following data:
  • The int n: the number of robots.
  • The String[] r: the strategies of the first few robots. The value k can be determined as the length of any of these strategies.
  • The ints seed, pR, pP, and pS: parameters for a pseudorandom generator used to produce the rest of the input.

Use the pseudocode below to generate the strategies of all robots. 
        long now = seed;
        long a = 22222223;
        long b = 12345678;
        long mod = 1000000000 + 7;
        String[] input = new String[n];
        for(int i = 0; i < r.length; i++)
            input[i] = r[i];
        for(int i = r.length; i < n; i++)
        {
            String s = "";
            for(int j = 0; j < r[0].length(); j++)
            {
                if((now % (pR + pP + pS)) < pR)
                    s += "R";
                else if((now % (pR + pP + pS)) < pR + pP)
                    s += "P";
                else
                    s += "S";
                now = (now * a + b) % mod;
            }
            input[i] = s;
        }

Notes

  • The author's solution does not depend on any properties of the pseudorandom generator. It would solve any input of allowed size within the given limits.

Constraints

  • n will be between 1 and 100,000, inclusive.
  • k will be between 1 and 18, inclusive.
  • r will contain between 1 and min(n, 1000) elements, inclusive.
  • Each element of r will contain exactly k elements.
  • Each character in r will be one of 'R', 'P', 'S'.
  • seed will be between 0 and 1,000,000,006, inclusive.
  • pR, pP, pS will be between 0 and 1,000, inclusive.
  • pR + pP + pS > 0.
Examples
0)
100000
{"RRRRRRRRRRRRRRRRRR","RRRRRRRRRRRRRRRRRP","RRRRRRRRRRRRRRRRPP","RRRRRRRRRRRRRRRRPS","RRRRRRRRRRRRRRRRSP","RRRRRRRRRRRRRRRPRS","RRRRRRRRRRRRRRRPPP","RRRRRRRRRRRRRRRSRP","RRRRRRRRRRRRRRPRRP","RRRRRRRRRRRRRRPRRS","RRRRRRRRRRRRRRPRPS","RRRRRRRRRRRRRRPPSS","RRRRRRRRRRRRRRSRRP","RRRRRRRRRRRRRRSRSP","RRRRRRRRRRRRRRSSPP","RRRRRRRRRRRRRPRPRP","RRRRRRRRRRRRRPPRSS","RRRRRRRRRRRRRPSRPS","RRRRRRRRRRRRRSPRSP","RRRRRRRRRRRRRSSRPP","RRRRRRRRRRRRPPPPPP","RRRRRRRRRRRRPPPSSS","RRRRRRRRRRRRSSSPPP","RRRRRRRRRRRPRRRRRS","RRRRRRRRRRRPRRPRRP","RRRRRRRRRRRPRPPRSP","RRRRRRRRRRRPRPPPRP","RRRRRRRRRRRPPRRRSS","RRRRRRRRRRRPPRPSSP","RRRRRRRRRRRPPPRSSS","RRRRRRRRRRRPSRRRPS","RRRRRRRRRRRPSRPPRP","RRRRRRRRRRRPSRPPPS","RRRRRRRRRRRPSSRPPS","RRRRRRRRRRRSRRRRRP","RRRRRRRRRRRSPPRSSP","RRRRRRRRRRRSSSRPPP","RRRRRRRRRRPRRPPRPS","RRRRRRRRRRPRPSPSRS","RRRRRRRRRRPPRRRRSS","RRRRRRRRRRPPRPPRPP","RRRRRRRRRRPPPRRPPP","RRRRRRRRRRPSRPPPPS","RRRRRRRRRRPSRPSRPS","RRRRRRRRRRPSSPSPPS","RRRRRRRRRRSRRSSRSP","RRRRRRRRRRSRSPSPRP","RRRRRRRRRRSPRSPRSP","RRRRRRRRRRSPRSSSSP","RRRRRRRRRRSPPSPSSP","RRRRRRRRRRSSRRRRPP","RRRRRRRRRPRRRSSSPP","RRRRRRRRRPRPPPSPRS","RRRRRRRRRPRPSPPSRP","RRRRRRRRRPRSPRSPRS","RRRRRRRRRPPPRRRSSS","RRRRRRRRRPPPPPPPPP","RRRRRRRRRPPSSPSRPS","RRRRRRRRRPPSSSRRRP","RRRRRRRRRSRPSRPSRP","RRRRRRRRRSPRSPSSPP","RRRRRRRRRSSSRRRPPP","RRRRRRRRPRRRRRRRRP","RRRRRRRRPRRRRRPRRS","RRRRRRRRPRRPRRSRRS","RRRRRRRRPRPRRRPRSS","RRRRRRRRPRPPSPSPPS","RRRRRRRRPRPSPPPSPS","RRRRRRRRPRSRRRRRPP","RRRRRRRRPRSPSSSPSS","RRRRRRRRPRSSPSPSSS","RRRRRRRRPPRPPSSPPS","RRRRRRRRPPPRRRRSSP","RRRRRRRRPPSSPRPPPS","RRRRRRRRPSRPSSSSPS","RRRRRRRRPSSRRRRPPP","RRRRRRRRSRRSRRPRRP","RRRRRRRRSRPSPPPSPP","RRRRRRRRSRSRRRSRPP","RRRRRRRPRRRPRPRRSS","RRRRRRRPRPRPRSRSRS","RRRRRRRPRPPPPPPPRP","RRRRRRRPPRRPRRSRPS","RRRRRRRPPPRRRRPSPS","RRRRRRRPPPRRRPRSSP","RRRRRRRPPPSRRRPSSS","RRRRRRRPSRRRRRRRPS","RRRRRRRPSRRSRRPRPP","RRRRRRRPSSRPRRRPPP","RRRRRRRSRRRSRSRRPP","RRRRRRRSRSRSRPRPRP","RRRRRRRSPRRRRRRRSP","RRRRRRRSPSPRRRRPPP","RRRRRRRSSSPRRRSPPP","RRRRRRPRPRPRPRRSSP","RRRRRRPRPRPSPRRSSS","RRRRRRPPRRSPPRRSSS","RRRRRRPPPRRRRRRPPP","RRRRRRPPPRRRPPPSSS","RRRRRRPPPPPPSSSSSS","RRRRRRPPPPPSPSSSSS","RRRRRRPPPPPSSPSSSS","RRRRRRPPPPPSSSPSSS","RRRRRRPPPPPSSSSSSP","RRRRRRPPPPSSSPPSSS","RRRRRRPPPSSSPPPSSS","RRRRRRPPSRPRRSRPSS","RRRRRRPPSPRRSRRSPS","RRRRRRPPSPPPSSSSSP","RRRRRRPPSPPSPSSPSS","RRRRRRPPSSSSPPPSSP","RRRRRRPSRRPSRRRPPP","RRRRRRPSPSPSPSPSPS","RRRRRRPSSRRPRPRPRP","RRRRRRPSSRRSRRPPSP","RRRRRRPSSRSRRPRPPS","RRRRRRPSSPPPSSSSPP","RRRRRRSSRRPSSRRPPP","RRRRRRSSSRRRSSSPPP","RRRRRRSSSSSSPPPPPP","RRRRRPRRRRRPRRRRRP","RRRRRPRRPPRPRRSSRP","RRRRRPRRSRRRRRPRRS","RRRRRPRRSSRPRRPPRP","RRRRRPRPRRRPRRRRPP","RRRRRPRPRPRPRSPSRS","RRRRRPRPRPPPRSRSSP","RRRRRPRPPRRPRSSRRP","RRRRRPRPPPPSSPSSSS","RRRRRPRPPPSPPSSSSS","RRRRRPRPPPSPSSSPSS","RRRRRPRPPPSPSSSSSP","RRRRRPRPPSPPSSSSSP","RRRRRPRPPSPSPSSSPS","RRRRRPRPPSPSSSPSPS","RRRRRPRPPSSPSPPSSS","RRRRRPRPSPPSPPSPRS","RRRRRPRSRSRSRPPPRP","RRRRRPRSRSSPRPRPPP","RRRRRPRSSRRPRPPRRP","RRRRRPPRRPPPSRRSSP","RRRRRPPRPPPSSSSPSS","RRRRRPPRPPSPPSSSSS","RRRRRPPRPPSSPPSSSS","RRRRRPPRPSPPRRSSSP","RRRRRPPRPSPPSPSSSS","RRRRRPPRSSPPSSSSPP","RRRRRPPRSSSPPSPSSP","RRRRRPPPRPSPSPSSSS","RRRRRPPPPPSSSRPSSS","RRRRRPPPPSPSRSPSSS","RRRRRPPPSRPSSSSPPS","RRRRRPPPSPPRSSPSSS","RRRRRPPSRPPSSSPSPS","RRRRRPPSPSSSPPRSPS","RRRRRPSRRSSPPRRPPP","RRRRRPSPRPPSSSSPSP","RRRRRPSSRRPSSRPPPP","RRRRRPSSPSPPSSSRPP","RRRRRSRRPRRRRRSRRP","RRRRRSRPSPPSPPSPRP","RRRRRSSSPRSSSPPPPP","RRRRRSSSPSRSPSPPPP","RRRRRSSSPSSRPPSPPP","RRRRPRRPPPSRRPPSSS","RRRRPRRSSSPRRPSPPP","RRRRPRPRPRPRPSPSRS","RRRRPRPSPSPSPSPSRS","RRRRPRSRPSPSPSPPSS","RRRRPPRRRRPPRRRRPP","RRRRPPRRSRPRRRPRPS","RRRRPPRPSRPSPPSSSS","RRRRPPRPSPPSSPSRSS","RRRRPPRSPRSPPSPSSS","RRRRPPRSPPSPSSPRSS","RRRRPPRSSRSPPSPSSP","RRRRPPRSSPPSSPSRPS","RRRRPPPRRRPPRRRPPP","RRRRPPPRRRPPPPRSSP","RRRRPPPRRSSPPPSSSS","RRRRPPPRSSPPRPSSSS","RRRRPPPPRSSPRPRSSP","RRRRPPPPRSSPPRSSSS","RRRRPPPSRSPPRSPSSS","RRRRPPPSPSSPRRSSSP","RRRRPPSRRPPSRRPPPP","RRRRPPSRRPPSSSPPSS","RRRRPSRRRRPSRRRRPS","RRRRPSRRPRPRRRSRPP","RRRRPSRPPRPSSSSPPS","RRRRPSRPPPPSRSSSPS","RRRRPSRPSRPSSSSPPP","RRRRPSRSSSPSRPPPPS","RRRRPSPRPPPSSRSSPS","RRRRPSPPSPRRSPSSPS","RRRRPSSRRPSSSSPPPP","RRRRPSSRPRPSSRPPPP","RRRRPSSRSRSPSPSPPP","RRRRPSSRSPSSRPPPPS","RRRRPSSRSSPSPRPPPS","RRRRPSSPSSRRPPSPPS","RRRRSRPRSPSPSPSSPP","RRRRSRSRSRSRSPSPRP","RRRRSRSPSPSPSPSPRP","RRRRSPRRRRSPRRRRSP","RRRRSPRPPRSPSSSPSP","RRRRSPRPPPSPRSSSSP","RRRRSPRSPSSPPSSRPP","RRRRSPRSSSSPRPPPSP","RRRRSPSSRRPSSSPPPP","RRRRSSRPSSPSPPSRPP","RRRRSSRSPRSPSSPPPP","RRRPRPRPSPRSPSRSRS","RRRPRPPSSPRSPPSSRS","RRRPRPSRPPPSSRPSSS","RRRPRPSRSSRPSPPSSP","RRRPRPSPRPSPSRPSSS","RRRPRPSPRSRPRSPSRS","RRRPRSRRRPRSRRRPRS","RRRPRSRPRPRSRRRPPS","RRRPRSRSRSRSPPSPRP","RRRPRSRSSSRPPSSPPP","RRRPRSPRPPPSSRSPSS","RRRPRSPRSPSSSPSPRP","RRRPRSSRSPSSPRPPPS","RRRPPRRRPPPRRPPPSS","RRRPPRRRSSPPPRRPPP","RRRPPRRPPPSSRPRPSS","RRRPPRRPPPSSSRPSSS","RRRPPRSRPPPSSPRSSS","RRRPPPRRRPPPRRRPPP","RRRPPPRRSPPRRRPPPS","RRRPPPSSSRRRPPPSSS","RRRPPSRRPPPRRRSPPP","RRRPPSRSRPRSRPRPSS","RRRPPSPSSRRRPPSPSS","RRRPPSSSPRRRPPSSSP","RRRPSRRSSSPRPSSPPP","RRRPSSRPRPRSRSRPPS","RRRSRPRRRSRPRRRSRP","RRRSRPRPRSRPRRRSPP","RRRSRPRSRSRSSPPPRP","RRRSRPPRPSPPSRSSSP","RRRSRPSRPSSPSPSPRP","RRRSRPSRSSSPPRPSPP","RRRSRSPRSSSPPRSPPP","RRRSPRRRSSSPPSSPPP","RRRSPRPRSSPRPRSPPP","RRRSPPRSRSRPRPRSSP","RRRSSPRPRSRPRSRSPP","RRRSSSPPPRRRSSSPPP","RRPRRPRRPRRPRRPRRP","RRPRRPRRPRPSRPSRPS","RRPRRPRRPPSSPSSPSS","RRPRRPRRPSPSSPSSPS","RRPRRPRRPSSPSSPSSP","RRPRRPRRSRSSRSSRSP","RRPRRPRRSPSSPSSPSP","RRPRRPRRSSPSSPSSPP","RRPRRPRPSRPSSPSSPS","RRPRRPRSPRSPPSSPSS","RRPRRPRSPSSPSSPSRP","RRPRRPRSSPSPRSSPSP","RRPRRPSRPSPSSRPSPS","RRPRPSRRPRPSRRPRPS","RRPRPSPRPSPSRSPSRS","RRPRPSPSPRRSPSPSRS","RRPRPSSPSRRPRPSSPS","RRPRSPPSSRRPRSPPSS","RRPPSSRRPPSSRRPPSS","RRPSRSRSPSPSPRPRPS","RRPSRSPSPRRSPSPRPS","RRPSPSRRPSPSRRPSPS","RRPSSPRRPSSPRRPSSP","RRSRSPRRSRSPRRSRSP","RRSPSPRRSPSPRRSPSP","RRSSPPRRSSPPRRSSPP","RPRPRPRPRPRPRPRPRP","RPRSPSRPRSPSRPRSPS","RPSRPSRPSRPSRPSRPS","RSPRSPRSPRSPRSPRSP"}
1213
1
1
1
Returns: 241395
1)
100000
{"RRRRRRRRRRRRRRRRRR","RRRRRRRRRRRRRRRRRP","RRRRRRRRRRRRRRRRPP","RRRRRRRRRRRRRRRRPS","RRRRRRRRRRRRRRRRSP","RRRRRRRRRRRRRRRPRS","RRRRRRRRRRRRRRRPPP","RRRRRRRRRRRRRRRSRP","RRRRRRRRRRRRRRPRRP","RRRRRRRRRRRRRRPRRS","RRRRRRRRRRRRRRPRPS","RRRRRRRRRRRRRRPPSS","RRRRRRRRRRRRRRSRRP","RRRRRRRRRRRRRRSRSP","RRRRRRRRRRRRRRSSPP","RRRRRRRRRRRRRPRPRP","RRRRRRRRRRRRRPPRSS","RRRRRRRRRRRRRPSRPS","RRRRRRRRRRRRRSPRSP","RRRRRRRRRRRRRSSRPP","RRRRRRRRRRRRPPPPPP","RRRRRRRRRRRRPPPSSS","RRRRRRRRRRRRSSSPPP","RRRRRRRRRRRPRRRRRS","RRRRRRRRRRRPRRPRRP","RRRRRRRRRRRPRPPRSP","RRRRRRRRRRRPRPPPRP","RRRRRRRRRRRPPRRRSS","RRRRRRRRRRRPPRPSSP","RRRRRRRRRRRPPPRSSS","RRRRRRRRRRRPSRRRPS","RRRRRRRRRRRPSRPPRP","RRRRRRRRRRRPSRPPPS","RRRRRRRRRRRPSSRPPS","RRRRRRRRRRRSRRRRRP","RRRRRRRRRRRSPPRSSP","RRRRRRRRRRRSSSRPPP","RRRRRRRRRRPRRPPRPS","RRRRRRRRRRPRPSPSRS","RRRRRRRRRRPPRRRRSS","RRRRRRRRRRPPRPPRPP","RRRRRRRRRRPPPRRPPP","RRRRRRRRRRPSRPPPPS","RRRRRRRRRRPSRPSRPS","RRRRRRRRRRPSSPSPPS","RRRRRRRRRRSRRSSRSP","RRRRRRRRRRSRSPSPRP","RRRRRRRRRRSPRSPRSP","RRRRRRRRRRSPRSSSSP","RRRRRRRRRRSPPSPSSP","RRRRRRRRRRSSRRRRPP","RRRRRRRRRPRRRSSSPP","RRRRRRRRRPRPPPSPRS","RRRRRRRRRPRPSPPSRP","RRRRRRRRRPRSPRSPRS","RRRRRRRRRPPPRRRSSS","RRRRRRRRRPPPPPPPPP","RRRRRRRRRPPSSPSRPS","RRRRRRRRRPPSSSRRRP","RRRRRRRRRSRPSRPSRP","RRRRRRRRRSPRSPSSPP","RRRRRRRRRSSSRRRPPP","RRRRRRRRPRRRRRRRRP","RRRRRRRRPRRRRRPRRS","RRRRRRRRPRRPRRSRRS","RRRRRRRRPRPRRRPRSS","RRRRRRRRPRPPSPSPPS","RRRRRRRRPRPSPPPSPS","RRRRRRRRPRSRRRRRPP","RRRRRRRRPRSPSSSPSS","RRRRRRRRPRSSPSPSSS","RRRRRRRRPPRPPSSPPS","RRRRRRRRPPPRRRRSSP","RRRRRRRRPPSSPRPPPS","RRRRRRRRPSRPSSSSPS","RRRRRRRRPSSRRRRPPP","RRRRRRRRSRRSRRPRRP","RRRRRRRRSRPSPPPSPP","RRRRRRRRSRSRRRSRPP","RRRRRRRPRRRPRPRRSS","RRRRRRRPRPRPRSRSRS","RRRRRRRPRPPPPPPPRP","RRRRRRRPPRRPRRSRPS","RRRRRRRPPPRRRRPSPS","RRRRRRRPPPRRRPRSSP","RRRRRRRPPPSRRRPSSS","RRRRRRRPSRRRRRRRPS","RRRRRRRPSRRSRRPRPP","RRRRRRRPSSRPRRRPPP","RRRRRRRSRRRSRSRRPP","RRRRRRRSRSRSRPRPRP","RRRRRRRSPRRRRRRRSP","RRRRRRRSPSPRRRRPPP","RRRRRRRSSSPRRRSPPP","RRRRRRPRPRPRPRRSSP","RRRRRRPRPRPSPRRSSS","RRRRRRPPRRSPPRRSSS","RRRRRRPPPRRRRRRPPP","RRRRRRPPPRRRPPPSSS","RRRRRRPPPPPPSSSSSS","RRRRRRPPPPPSPSSSSS","RRRRRRPPPPPSSPSSSS","RRRRRRPPPPPSSSPSSS","RRRRRRPPPPPSSSSSSP","RRRRRRPPPPSSSPPSSS","RRRRRRPPPSSSPPPSSS","RRRRRRPPSRPRRSRPSS","RRRRRRPPSPRRSRRSPS","RRRRRRPPSPPPSSSSSP","RRRRRRPPSPPSPSSPSS","RRRRRRPPSSSSPPPSSP","RRRRRRPSRRPSRRRPPP","RRRRRRPSPSPSPSPSPS","RRRRRRPSSRRPRPRPRP","RRRRRRPSSRRSRRPPSP","RRRRRRPSSRSRRPRPPS","RRRRRRPSSPPPSSSSPP","RRRRRRSSRRPSSRRPPP","RRRRRRSSSRRRSSSPPP","RRRRRRSSSSSSPPPPPP","RRRRRPRRRRRPRRRRRP","RRRRRPRRPPRPRRSSRP","RRRRRPRRSRRRRRPRRS","RRRRRPRRSSRPRRPPRP","RRRRRPRPRRRPRRRRPP","RRRRRPRPRPRPRSPSRS","RRRRRPRPRPPPRSRSSP","RRRRRPRPPRRPRSSRRP","RRRRRPRPPPPSSPSSSS","RRRRRPRPPPSPPSSSSS","RRRRRPRPPPSPSSSPSS","RRRRRPRPPPSPSSSSSP","RRRRRPRPPSPPSSSSSP","RRRRRPRPPSPSPSSSPS","RRRRRPRPPSPSSSPSPS","RRRRRPRPPSSPSPPSSS","RRRRRPRPSPPSPPSPRS","RRRRRPRSRSRSRPPPRP","RRRRRPRSRSSPRPRPPP","RRRRRPRSSRRPRPPRRP","RRRRRPPRRPPPSRRSSP","RRRRRPPRPPPSSSSPSS","RRRRRPPRPPSPPSSSSS","RRRRRPPRPPSSPPSSSS","RRRRRPPRPSPPRRSSSP","RRRRRPPRPSPPSPSSSS","RRRRRPPRSSPPSSSSPP","RRRRRPPRSSSPPSPSSP","RRRRRPPPRPSPSPSSSS","RRRRRPPPPPSSSRPSSS","RRRRRPPPPSPSRSPSSS","RRRRRPPPSRPSSSSPPS","RRRRRPPPSPPRSSPSSS","RRRRRPPSRPPSSSPSPS","RRRRRPPSPSSSPPRSPS","RRRRRPSRRSSPPRRPPP","RRRRRPSPRPPSSSSPSP","RRRRRPSSRRPSSRPPPP","RRRRRPSSPSPPSSSRPP","RRRRRSRRPRRRRRSRRP","RRRRRSRPSPPSPPSPRP","RRRRRSSSPRSSSPPPPP","RRRRRSSSPSRSPSPPPP","RRRRRSSSPSSRPPSPPP","RRRRPRRPPPSRRPPSSS","RRRRPRRSSSPRRPSPPP","RRRRPRPRPRPRPSPSRS","RRRRPRPSPSPSPSPSRS","RRRRPRSRPSPSPSPPSS","RRRRPPRRRRPPRRRRPP","RRRRPPRRSRPRRRPRPS","RRRRPPRPSRPSPPSSSS","RRRRPPRPSPPSSPSRSS","RRRRPPRSPRSPPSPSSS","RRRRPPRSPPSPSSPRSS","RRRRPPRSSRSPPSPSSP","RRRRPPRSSPPSSPSRPS","RRRRPPPRRRPPRRRPPP","RRRRPPPRRRPPPPRSSP","RRRRPPPRRSSPPPSSSS","RRRRPPPRSSPPRPSSSS","RRRRPPPPRSSPRPRSSP","RRRRPPPPRSSPPRSSSS","RRRRPPPSRSPPRSPSSS","RRRRPPPSPSSPRRSSSP","RRRRPPSRRPPSRRPPPP","RRRRPPSRRPPSSSPPSS","RRRRPSRRRRPSRRRRPS","RRRRPSRRPRPRRRSRPP","RRRRPSRPPRPSSSSPPS","RRRRPSRPPPPSRSSSPS","RRRRPSRPSRPSSSSPPP","RRRRPSRSSSPSRPPPPS","RRRRPSPRPPPSSRSSPS","RRRRPSPPSPRRSPSSPS","RRRRPSSRRPSSSSPPPP","RRRRPSSRPRPSSRPPPP","RRRRPSSRSRSPSPSPPP","RRRRPSSRSPSSRPPPPS","RRRRPSSRSSPSPRPPPS","RRRRPSSPSSRRPPSPPS","RRRRSRPRSPSPSPSSPP","RRRRSRSRSRSRSPSPRP","RRRRSRSPSPSPSPSPRP","RRRRSPRRRRSPRRRRSP","RRRRSPRPPRSPSSSPSP","RRRRSPRPPPSPRSSSSP","RRRRSPRSPSSPPSSRPP","RRRRSPRSSSSPRPPPSP","RRRRSPSSRRPSSSPPPP","RRRRSSRPSSPSPPSRPP","RRRRSSRSPRSPSSPPPP","RRRPRPRPSPRSPSRSRS","RRRPRPPSSPRSPPSSRS","RRRPRPSRPPPSSRPSSS","RRRPRPSRSSRPSPPSSP","RRRPRPSPRPSPSRPSSS","RRRPRPSPRSRPRSPSRS","RRRPRSRRRPRSRRRPRS","RRRPRSRPRPRSRRRPPS","RRRPRSRSRSRSPPSPRP","RRRPRSRSSSRPPSSPPP","RRRPRSPRPPPSSRSPSS","RRRPRSPRSPSSSPSPRP","RRRPRSSRSPSSPRPPPS","RRRPPRRRPPPRRPPPSS","RRRPPRRRSSPPPRRPPP","RRRPPRRPPPSSRPRPSS","RRRPPRRPPPSSSRPSSS","RRRPPRSRPPPSSPRSSS","RRRPPPRRRPPPRRRPPP","RRRPPPRRSPPRRRPPPS","RRRPPPSSSRRRPPPSSS","RRRPPSRRPPPRRRSPPP","RRRPPSRSRPRSRPRPSS","RRRPPSPSSRRRPPSPSS","RRRPPSSSPRRRPPSSSP","RRRPSRRSSSPRPSSPPP","RRRPSSRPRPRSRSRPPS","RRRSRPRRRSRPRRRSRP","RRRSRPRPRSRPRRRSPP","RRRSRPRSRSRSSPPPRP","RRRSRPPRPSPPSRSSSP","RRRSRPSRPSSPSPSPRP","RRRSRPSRSSSPPRPSPP","RRRSRSPRSSSPPRSPPP","RRRSPRRRSSSPPSSPPP","RRRSPRPRSSPRPRSPPP","RRRSPPRSRSRPRPRSSP","RRRSSPRPRSRPRSRSPP","RRRSSSPPPRRRSSSPPP","RRPRRPRRPRRPRRPRRP","RRPRRPRRPRPSRPSRPS","RRPRRPRRPPSSPSSPSS","RRPRRPRRPSPSSPSSPS","RRPRRPRRPSSPSSPSSP","RRPRRPRRSRSSRSSRSP","RRPRRPRRSPSSPSSPSP","RRPRRPRRSSPSSPSSPP","RRPRRPRPSRPSSPSSPS","RRPRRPRSPRSPPSSPSS","RRPRRPRSPSSPSSPSRP","RRPRRPRSSPSPRSSPSP","RRPRRPSRPSPSSRPSPS","RRPRPSRRPRPSRRPRPS","RRPRPSPRPSPSRSPSRS","RRPRPSPSPRRSPSPSRS","RRPRPSSPSRRPRPSSPS","RRPRSPPSSRRPRSPPSS","RRPPSSRRPPSSRRPPSS","RRPSRSRSPSPSPRPRPS","RRPSRSPSPRRSPSPRPS","RRPSPSRRPSPSRRPSPS","RRPSSPRRPSSPRRPSSP","RRSRSPRRSRSPRRSRSP","RRSPSPRRSPSPRRSPSP","RRSSPPRRSSPPRRSSPP","RPRPRPRPRPRPRPRPRP","RPRSPSRPRSPSRPRSPS","RPSRPSRPSRPSRPSRPS","RSPRSPRSPRSPRSPRSP"}
4127872
1
1000
1000
Returns: 659597
2)
100000
{"RRRRRRRRRRRRRRRRRR","RRRRRRRRRRRRRRRRRP","RRRRRRRRRRRRRRRRPP","RRRRRRRRRRRRRRRRPS","RRRRRRRRRRRRRRRRSP","RRRRRRRRRRRRRRRPRS","RRRRRRRRRRRRRRRPPP","RRRRRRRRRRRRRRRSRP","RRRRRRRRRRRRRRPRRP","RRRRRRRRRRRRRRPRRS","RRRRRRRRRRRRRRPRPS","RRRRRRRRRRRRRRPPSS","RRRRRRRRRRRRRRSRRP","RRRRRRRRRRRRRRSRSP","RRRRRRRRRRRRRRSSPP","RRRRRRRRRRRRRPRPRP","RRRRRRRRRRRRRPPRSS","RRRRRRRRRRRRRPSRPS","RRRRRRRRRRRRRSPRSP","RRRRRRRRRRRRRSSRPP","RRRRRRRRRRRRPPPPPP","RRRRRRRRRRRRPPPSSS","RRRRRRRRRRRRSSSPPP","RRRRRRRRRRRPRRRRRS","RRRRRRRRRRRPRRPRRP","RRRRRRRRRRRPRPPRSP","RRRRRRRRRRRPRPPPRP","RRRRRRRRRRRPPRRRSS","RRRRRRRRRRRPPRPSSP","RRRRRRRRRRRPPPRSSS","RRRRRRRRRRRPSRRRPS","RRRRRRRRRRRPSRPPRP","RRRRRRRRRRRPSRPPPS","RRRRRRRRRRRPSSRPPS","RRRRRRRRRRRSRRRRRP","RRRRRRRRRRRSPPRSSP","RRRRRRRRRRRSSSRPPP","RRRRRRRRRRPRRPPRPS","RRRRRRRRRRPRPSPSRS","RRRRRRRRRRPPRRRRSS","RRRRRRRRRRPPRPPRPP","RRRRRRRRRRPPPRRPPP","RRRRRRRRRRPSRPPPPS","RRRRRRRRRRPSRPSRPS","RRRRRRRRRRPSSPSPPS","RRRRRRRRRRSRRSSRSP","RRRRRRRRRRSRSPSPRP","RRRRRRRRRRSPRSPRSP","RRRRRRRRRRSPRSSSSP","RRRRRRRRRRSPPSPSSP","RRRRRRRRRRSSRRRRPP","RRRRRRRRRPRRRSSSPP","RRRRRRRRRPRPPPSPRS","RRRRRRRRRPRPSPPSRP","RRRRRRRRRPRSPRSPRS","RRRRRRRRRPPPRRRSSS","RRRRRRRRRPPPPPPPPP","RRRRRRRRRPPSSPSRPS","RRRRRRRRRPPSSSRRRP","RRRRRRRRRSRPSRPSRP","RRRRRRRRRSPRSPSSPP","RRRRRRRRRSSSRRRPPP","RRRRRRRRPRRRRRRRRP","RRRRRRRRPRRRRRPRRS","RRRRRRRRPRRPRRSRRS","RRRRRRRRPRPRRRPRSS","RRRRRRRRPRPPSPSPPS","RRRRRRRRPRPSPPPSPS","RRRRRRRRPRSRRRRRPP","RRRRRRRRPRSPSSSPSS","RRRRRRRRPRSSPSPSSS","RRRRRRRRPPRPPSSPPS","RRRRRRRRPPPRRRRSSP","RRRRRRRRPPSSPRPPPS","RRRRRRRRPSRPSSSSPS","RRRRRRRRPSSRRRRPPP","RRRRRRRRSRRSRRPRRP","RRRRRRRRSRPSPPPSPP","RRRRRRRRSRSRRRSRPP","RRRRRRRPRRRPRPRRSS","RRRRRRRPRPRPRSRSRS","RRRRRRRPRPPPPPPPRP","RRRRRRRPPRRPRRSRPS","RRRRRRRPPPRRRRPSPS","RRRRRRRPPPRRRPRSSP","RRRRRRRPPPSRRRPSSS","RRRRRRRPSRRRRRRRPS","RRRRRRRPSRRSRRPRPP","RRRRRRRPSSRPRRRPPP","RRRRRRRSRRRSRSRRPP","RRRRRRRSRSRSRPRPRP","RRRRRRRSPRRRRRRRSP","RRRRRRRSPSPRRRRPPP","RRRRRRRSSSPRRRSPPP","RRRRRRPRPRPRPRRSSP","RRRRRRPRPRPSPRRSSS","RRRRRRPPRRSPPRRSSS","RRRRRRPPPRRRRRRPPP","RRRRRRPPPRRRPPPSSS","RRRRRRPPPPPPSSSSSS","RRRRRRPPPPPSPSSSSS","RRRRRRPPPPPSSPSSSS","RRRRRRPPPPPSSSPSSS","RRRRRRPPPPPSSSSSSP","RRRRRRPPPPSSSPPSSS","RRRRRRPPPSSSPPPSSS","RRRRRRPPSRPRRSRPSS","RRRRRRPPSPRRSRRSPS","RRRRRRPPSPPPSSSSSP","RRRRRRPPSPPSPSSPSS","RRRRRRPPSSSSPPPSSP","RRRRRRPSRRPSRRRPPP","RRRRRRPSPSPSPSPSPS","RRRRRRPSSRRPRPRPRP","RRRRRRPSSRRSRRPPSP","RRRRRRPSSRSRRPRPPS","RRRRRRPSSPPPSSSSPP","RRRRRRSSRRPSSRRPPP","RRRRRRSSSRRRSSSPPP","RRRRRRSSSSSSPPPPPP","RRRRRPRRRRRPRRRRRP","RRRRRPRRPPRPRRSSRP","RRRRRPRRSRRRRRPRRS","RRRRRPRRSSRPRRPPRP","RRRRRPRPRRRPRRRRPP","RRRRRPRPRPRPRSPSRS","RRRRRPRPRPPPRSRSSP","RRRRRPRPPRRPRSSRRP","RRRRRPRPPPPSSPSSSS","RRRRRPRPPPSPPSSSSS","RRRRRPRPPPSPSSSPSS","RRRRRPRPPPSPSSSSSP","RRRRRPRPPSPPSSSSSP","RRRRRPRPPSPSPSSSPS","RRRRRPRPPSPSSSPSPS","RRRRRPRPPSSPSPPSSS","RRRRRPRPSPPSPPSPRS","RRRRRPRSRSRSRPPPRP","RRRRRPRSRSSPRPRPPP","RRRRRPRSSRRPRPPRRP","RRRRRPPRRPPPSRRSSP","RRRRRPPRPPPSSSSPSS","RRRRRPPRPPSPPSSSSS","RRRRRPPRPPSSPPSSSS","RRRRRPPRPSPPRRSSSP","RRRRRPPRPSPPSPSSSS","RRRRRPPRSSPPSSSSPP","RRRRRPPRSSSPPSPSSP","RRRRRPPPRPSPSPSSSS","RRRRRPPPPPSSSRPSSS","RRRRRPPPPSPSRSPSSS","RRRRRPPPSRPSSSSPPS","RRRRRPPPSPPRSSPSSS","RRRRRPPSRPPSSSPSPS","RRRRRPPSPSSSPPRSPS","RRRRRPSRRSSPPRRPPP","RRRRRPSPRPPSSSSPSP","RRRRRPSSRRPSSRPPPP","RRRRRPSSPSPPSSSRPP","RRRRRSRRPRRRRRSRRP","RRRRRSRPSPPSPPSPRP","RRRRRSSSPRSSSPPPPP","RRRRRSSSPSRSPSPPPP","RRRRRSSSPSSRPPSPPP","RRRRPRRPPPSRRPPSSS","RRRRPRRSSSPRRPSPPP","RRRRPRPRPRPRPSPSRS","RRRRPRPSPSPSPSPSRS","RRRRPRSRPSPSPSPPSS","RRRRPPRRRRPPRRRRPP","RRRRPPRRSRPRRRPRPS","RRRRPPRPSRPSPPSSSS","RRRRPPRPSPPSSPSRSS","RRRRPPRSPRSPPSPSSS","RRRRPPRSPPSPSSPRSS","RRRRPPRSSRSPPSPSSP","RRRRPPRSSPPSSPSRPS","RRRRPPPRRRPPRRRPPP","RRRRPPPRRRPPPPRSSP","RRRRPPPRRSSPPPSSSS","RRRRPPPRSSPPRPSSSS","RRRRPPPPRSSPRPRSSP","RRRRPPPPRSSPPRSSSS","RRRRPPPSRSPPRSPSSS","RRRRPPPSPSSPRRSSSP","RRRRPPSRRPPSRRPPPP","RRRRPPSRRPPSSSPPSS","RRRRPSRRRRPSRRRRPS","RRRRPSRRPRPRRRSRPP","RRRRPSRPPRPSSSSPPS","RRRRPSRPPPPSRSSSPS","RRRRPSRPSRPSSSSPPP","RRRRPSRSSSPSRPPPPS","RRRRPSPRPPPSSRSSPS","RRRRPSPPSPRRSPSSPS","RRRRPSSRRPSSSSPPPP","RRRRPSSRPRPSSRPPPP","RRRRPSSRSRSPSPSPPP","RRRRPSSRSPSSRPPPPS","RRRRPSSRSSPSPRPPPS","RRRRPSSPSSRRPPSPPS","RRRRSRPRSPSPSPSSPP","RRRRSRSRSRSRSPSPRP","RRRRSRSPSPSPSPSPRP","RRRRSPRRRRSPRRRRSP","RRRRSPRPPRSPSSSPSP","RRRRSPRPPPSPRSSSSP","RRRRSPRSPSSPPSSRPP","RRRRSPRSSSSPRPPPSP","RRRRSPSSRRPSSSPPPP","RRRRSSRPSSPSPPSRPP","RRRRSSRSPRSPSSPPPP","RRRPRPRPSPRSPSRSRS","RRRPRPPSSPRSPPSSRS","RRRPRPSRPPPSSRPSSS","RRRPRPSRSSRPSPPSSP","RRRPRPSPRPSPSRPSSS","RRRPRPSPRSRPRSPSRS","RRRPRSRRRPRSRRRPRS","RRRPRSRPRPRSRRRPPS","RRRPRSRSRSRSPPSPRP","RRRPRSRSSSRPPSSPPP","RRRPRSPRPPPSSRSPSS","RRRPRSPRSPSSSPSPRP","RRRPRSSRSPSSPRPPPS","RRRPPRRRPPPRRPPPSS","RRRPPRRRSSPPPRRPPP","RRRPPRRPPPSSRPRPSS","RRRPPRRPPPSSSRPSSS","RRRPPRSRPPPSSPRSSS","RRRPPPRRRPPPRRRPPP","RRRPPPRRSPPRRRPPPS","RRRPPPSSSRRRPPPSSS","RRRPPSRRPPPRRRSPPP","RRRPPSRSRPRSRPRPSS","RRRPPSPSSRRRPPSPSS","RRRPPSSSPRRRPPSSSP","RRRPSRRSSSPRPSSPPP","RRRPSSRPRPRSRSRPPS","RRRSRPRRRSRPRRRSRP","RRRSRPRPRSRPRRRSPP","RRRSRPRSRSRSSPPPRP","RRRSRPPRPSPPSRSSSP","RRRSRPSRPSSPSPSPRP","RRRSRPSRSSSPPRPSPP","RRRSRSPRSSSPPRSPPP","RRRSPRRRSSSPPSSPPP","RRRSPRPRSSPRPRSPPP","RRRSPPRSRSRPRPRSSP","RRRSSPRPRSRPRSRSPP","RRRSSSPPPRRRSSSPPP","RRPRRPRRPRRPRRPRRP","RRPRRPRRPRPSRPSRPS","RRPRRPRRPPSSPSSPSS","RRPRRPRRPSPSSPSSPS","RRPRRPRRPSSPSSPSSP","RRPRRPRRSRSSRSSRSP","RRPRRPRRSPSSPSSPSP","RRPRRPRRSSPSSPSSPP","RRPRRPRPSRPSSPSSPS","RRPRRPRSPRSPPSSPSS","RRPRRPRSPSSPSSPSRP","RRPRRPRSSPSPRSSPSP","RRPRRPSRPSPSSRPSPS","RRPRPSRRPRPSRRPRPS","RRPRPSPRPSPSRSPSRS","RRPRPSPSPRRSPSPSRS","RRPRPSSPSRRPRPSSPS","RRPRSPPSSRRPRSPPSS","RRPPSSRRPPSSRRPPSS","RRPSRSRSPSPSPRPRPS","RRPSRSPSPRRSPSPRPS","RRPSPSRRPSPSRRPSPS","RRPSSPRRPSSPRRPSSP","RRSRSPRRSRSPRRSRSP","RRSPSPRRSPSPRRSPSP","RRSSPPRRSSPPRRSSPP","RPRPRPRPRPRPRPRPRP","RPRSPSRPRSPSRPRSPS","RPSRPSRPSRPSRPSRPS","RSPRSPRSPRSPRSPRSP"}
412839
1
1
0
Returns: 554417
3)
100000
{"RRRRRRRRRRRRRRRRRR","RRRRRRRRRRRRRRRRRP","RRRRRRRRRRRRRRRRPP","RRRRRRRRRRRRRRRRPS","RRRRRRRRRRRRRRRRSP","RRRRRRRRRRRRRRRPRS","RRRRRRRRRRRRRRRPPP","RRRRRRRRRRRRRRRSRP","RRRRRRRRRRRRRRPRRP","RRRRRRRRRRRRRRPRRS","RRRRRRRRRRRRRRPRPS","RRRRRRRRRRRRRRPPSS","RRRRRRRRRRRRRRSRRP","RRRRRRRRRRRRRRSRSP","RRRRRRRRRRRRRRSSPP","RRRRRRRRRRRRRPRPRP","RRRRRRRRRRRRRPPRSS","RRRRRRRRRRRRRPSRPS","RRRRRRRRRRRRRSPRSP","RRRRRRRRRRRRRSSRPP","RRRRRRRRRRRRPPPPPP","RRRRRRRRRRRRPPPSSS","RRRRRRRRRRRRSSSPPP","RRRRRRRRRRRPRRRRRS","RRRRRRRRRRRPRRPRRP","RRRRRRRRRRRPRPPRSP","RRRRRRRRRRRPRPPPRP","RRRRRRRRRRRPPRRRSS","RRRRRRRRRRRPPRPSSP","RRRRRRRRRRRPPPRSSS","RRRRRRRRRRRPSRRRPS","RRRRRRRRRRRPSRPPRP","RRRRRRRRRRRPSRPPPS","RRRRRRRRRRRPSSRPPS","RRRRRRRRRRRSRRRRRP","RRRRRRRRRRRSPPRSSP","RRRRRRRRRRRSSSRPPP","RRRRRRRRRRPRRPPRPS","RRRRRRRRRRPRPSPSRS","RRRRRRRRRRPPRRRRSS","RRRRRRRRRRPPRPPRPP","RRRRRRRRRRPPPRRPPP","RRRRRRRRRRPSRPPPPS","RRRRRRRRRRPSRPSRPS","RRRRRRRRRRPSSPSPPS","RRRRRRRRRRSRRSSRSP","RRRRRRRRRRSRSPSPRP","RRRRRRRRRRSPRSPRSP","RRRRRRRRRRSPRSSSSP","RRRRRRRRRRSPPSPSSP","RRRRRRRRRRSSRRRRPP","RRRRRRRRRPRRRSSSPP","RRRRRRRRRPRPPPSPRS","RRRRRRRRRPRPSPPSRP","RRRRRRRRRPRSPRSPRS","RRRRRRRRRPPPRRRSSS","RRRRRRRRRPPPPPPPPP","RRRRRRRRRPPSSPSRPS","RRRRRRRRRPPSSSRRRP","RRRRRRRRRSRPSRPSRP","RRRRRRRRRSPRSPSSPP","RRRRRRRRRSSSRRRPPP","RRRRRRRRPRRRRRRRRP","RRRRRRRRPRRRRRPRRS","RRRRRRRRPRRPRRSRRS","RRRRRRRRPRPRRRPRSS","RRRRRRRRPRPPSPSPPS","RRRRRRRRPRPSPPPSPS","RRRRRRRRPRSRRRRRPP","RRRRRRRRPRSPSSSPSS","RRRRRRRRPRSSPSPSSS","RRRRRRRRPPRPPSSPPS","RRRRRRRRPPPRRRRSSP","RRRRRRRRPPSSPRPPPS","RRRRRRRRPSRPSSSSPS","RRRRRRRRPSSRRRRPPP","RRRRRRRRSRRSRRPRRP","RRRRRRRRSRPSPPPSPP","RRRRRRRRSRSRRRSRPP","RRRRRRRPRRRPRPRRSS","RRRRRRRPRPRPRSRSRS","RRRRRRRPRPPPPPPPRP","RRRRRRRPPRRPRRSRPS","RRRRRRRPPPRRRRPSPS","RRRRRRRPPPRRRPRSSP","RRRRRRRPPPSRRRPSSS","RRRRRRRPSRRRRRRRPS","RRRRRRRPSRRSRRPRPP","RRRRRRRPSSRPRRRPPP","RRRRRRRSRRRSRSRRPP","RRRRRRRSRSRSRPRPRP","RRRRRRRSPRRRRRRRSP","RRRRRRRSPSPRRRRPPP","RRRRRRRSSSPRRRSPPP","RRRRRRPRPRPRPRRSSP","RRRRRRPRPRPSPRRSSS","RRRRRRPPRRSPPRRSSS","RRRRRRPPPRRRRRRPPP","RRRRRRPPPRRRPPPSSS","RRRRRRPPPPPPSSSSSS","RRRRRRPPPPPSPSSSSS","RRRRRRPPPPPSSPSSSS","RRRRRRPPPPPSSSPSSS","RRRRRRPPPPPSSSSSSP","RRRRRRPPPPSSSPPSSS","RRRRRRPPPSSSPPPSSS","RRRRRRPPSRPRRSRPSS","RRRRRRPPSPRRSRRSPS","RRRRRRPPSPPPSSSSSP","RRRRRRPPSPPSPSSPSS","RRRRRRPPSSSSPPPSSP","RRRRRRPSRRPSRRRPPP","RRRRRRPSPSPSPSPSPS","RRRRRRPSSRRPRPRPRP","RRRRRRPSSRRSRRPPSP","RRRRRRPSSRSRRPRPPS","RRRRRRPSSPPPSSSSPP","RRRRRRSSRRPSSRRPPP","RRRRRRSSSRRRSSSPPP","RRRRRRSSSSSSPPPPPP","RRRRRPRRRRRPRRRRRP","RRRRRPRRPPRPRRSSRP","RRRRRPRRSRRRRRPRRS","RRRRRPRRSSRPRRPPRP","RRRRRPRPRRRPRRRRPP","RRRRRPRPRPRPRSPSRS","RRRRRPRPRPPPRSRSSP","RRRRRPRPPRRPRSSRRP","RRRRRPRPPPPSSPSSSS","RRRRRPRPPPSPPSSSSS","RRRRRPRPPPSPSSSPSS","RRRRRPRPPPSPSSSSSP","RRRRRPRPPSPPSSSSSP","RRRRRPRPPSPSPSSSPS","RRRRRPRPPSPSSSPSPS","RRRRRPRPPSSPSPPSSS","RRRRRPRPSPPSPPSPRS","RRRRRPRSRSRSRPPPRP","RRRRRPRSRSSPRPRPPP","RRRRRPRSSRRPRPPRRP","RRRRRPPRRPPPSRRSSP","RRRRRPPRPPPSSSSPSS","RRRRRPPRPPSPPSSSSS","RRRRRPPRPPSSPPSSSS","RRRRRPPRPSPPRRSSSP","RRRRRPPRPSPPSPSSSS","RRRRRPPRSSPPSSSSPP","RRRRRPPRSSSPPSPSSP","RRRRRPPPRPSPSPSSSS","RRRRRPPPPPSSSRPSSS","RRRRRPPPPSPSRSPSSS","RRRRRPPPSRPSSSSPPS","RRRRRPPPSPPRSSPSSS","RRRRRPPSRPPSSSPSPS","RRRRRPPSPSSSPPRSPS","RRRRRPSRRSSPPRRPPP","RRRRRPSPRPPSSSSPSP","RRRRRPSSRRPSSRPPPP","RRRRRPSSPSPPSSSRPP","RRRRRSRRPRRRRRSRRP","RRRRRSRPSPPSPPSPRP","RRRRRSSSPRSSSPPPPP","RRRRRSSSPSRSPSPPPP","RRRRRSSSPSSRPPSPPP","RRRRPRRPPPSRRPPSSS","RRRRPRRSSSPRRPSPPP","RRRRPRPRPRPRPSPSRS","RRRRPRPSPSPSPSPSRS","RRRRPRSRPSPSPSPPSS","RRRRPPRRRRPPRRRRPP","RRRRPPRRSRPRRRPRPS","RRRRPPRPSRPSPPSSSS","RRRRPPRPSPPSSPSRSS","RRRRPPRSPRSPPSPSSS","RRRRPPRSPPSPSSPRSS","RRRRPPRSSRSPPSPSSP","RRRRPPRSSPPSSPSRPS","RRRRPPPRRRPPRRRPPP","RRRRPPPRRRPPPPRSSP","RRRRPPPRRSSPPPSSSS","RRRRPPPRSSPPRPSSSS","RRRRPPPPRSSPRPRSSP","RRRRPPPPRSSPPRSSSS","RRRRPPPSRSPPRSPSSS","RRRRPPPSPSSPRRSSSP","RRRRPPSRRPPSRRPPPP","RRRRPPSRRPPSSSPPSS","RRRRPSRRRRPSRRRRPS","RRRRPSRRPRPRRRSRPP","RRRRPSRPPRPSSSSPPS","RRRRPSRPPPPSRSSSPS","RRRRPSRPSRPSSSSPPP","RRRRPSRSSSPSRPPPPS","RRRRPSPRPPPSSRSSPS","RRRRPSPPSPRRSPSSPS","RRRRPSSRRPSSSSPPPP","RRRRPSSRPRPSSRPPPP","RRRRPSSRSRSPSPSPPP","RRRRPSSRSPSSRPPPPS","RRRRPSSRSSPSPRPPPS","RRRRPSSPSSRRPPSPPS","RRRRSRPRSPSPSPSSPP","RRRRSRSRSRSRSPSPRP","RRRRSRSPSPSPSPSPRP","RRRRSPRRRRSPRRRRSP","RRRRSPRPPRSPSSSPSP","RRRRSPRPPPSPRSSSSP","RRRRSPRSPSSPPSSRPP","RRRRSPRSSSSPRPPPSP","RRRRSPSSRRPSSSPPPP","RRRRSSRPSSPSPPSRPP","RRRRSSRSPRSPSSPPPP","RRRPRPRPSPRSPSRSRS","RRRPRPPSSPRSPPSSRS","RRRPRPSRPPPSSRPSSS","RRRPRPSRSSRPSPPSSP","RRRPRPSPRPSPSRPSSS","RRRPRPSPRSRPRSPSRS","RRRPRSRRRPRSRRRPRS","RRRPRSRPRPRSRRRPPS","RRRPRSRSRSRSPPSPRP","RRRPRSRSSSRPPSSPPP","RRRPRSPRPPPSSRSPSS","RRRPRSPRSPSSSPSPRP","RRRPRSSRSPSSPRPPPS","RRRPPRRRPPPRRPPPSS","RRRPPRRRSSPPPRRPPP","RRRPPRRPPPSSRPRPSS","RRRPPRRPPPSSSRPSSS","RRRPPRSRPPPSSPRSSS","RRRPPPRRRPPPRRRPPP","RRRPPPRRSPPRRRPPPS","RRRPPPSSSRRRPPPSSS","RRRPPSRRPPPRRRSPPP","RRRPPSRSRPRSRPRPSS","RRRPPSPSSRRRPPSPSS","RRRPPSSSPRRRPPSSSP","RRRPSRRSSSPRPSSPPP","RRRPSSRPRPRSRSRPPS","RRRSRPRRRSRPRRRSRP","RRRSRPRPRSRPRRRSPP","RRRSRPRSRSRSSPPPRP","RRRSRPPRPSPPSRSSSP","RRRSRPSRPSSPSPSPRP","RRRSRPSRSSSPPRPSPP","RRRSRSPRSSSPPRSPPP","RRRSPRRRSSSPPSSPPP","RRRSPRPRSSPRPRSPPP","RRRSPPRSRSRPRPRSSP","RRRSSPRPRSRPRSRSPP","RRRSSSPPPRRRSSSPPP","RRPRRPRRPRRPRRPRRP","RRPRRPRRPRPSRPSRPS","RRPRRPRRPPSSPSSPSS","RRPRRPRRPSPSSPSSPS","RRPRRPRRPSSPSSPSSP","RRPRRPRRSRSSRSSRSP","RRPRRPRRSPSSPSSPSP","RRPRRPRRSSPSSPSSPP","RRPRRPRPSRPSSPSSPS","RRPRRPRSPRSPPSSPSS","RRPRRPRSPSSPSSPSRP","RRPRRPRSSPSPRSSPSP","RRPRRPSRPSPSSRPSPS","RRPRPSRRPRPSRRPRPS","RRPRPSPRPSPSRSPSRS","RRPRPSPSPRRSPSPSRS","RRPRPSSPSRRPRPSSPS","RRPRSPPSSRRPRSPPSS","RRPPSSRRPPSSRRPPSS","RRPSRSRSPSPSPRPRPS","RRPSRSPSPRRSPSPRPS","RRPSPSRRPSPSRRPSPS","RRPSSPRRPSSPRRPSSP","RRSRSPRRSRSPRRSRSP","RRSPSPRRSPSPRRSPSP","RRSSPPRRSSPPRRSSPP","RPRPRPRPRPRPRPRPRP","RPRSPSRPRSPSRPRSPS","RPSRPSRPSRPSRPSRPS","RSPRSPRSPRSPRSPRSP"}
129839
1
0
0
Returns: 203470174
4)
100000
{"RRRRRRRRRRRRRRRRRR","RRRRRRRRRRRRRRRRRP","RRRRRRRRRRRRRRRRPP","RRRRRRRRRRRRRRRRPS","RRRRRRRRRRRRRRRRSP","RRRRRRRRRRRRRRRPRS","RRRRRRRRRRRRRRRPPP","RRRRRRRRRRRRRRRSRP","RRRRRRRRRRRRRRPRRP","RRRRRRRRRRRRRRPRRS","RRRRRRRRRRRRRRPRPS","RRRRRRRRRRRRRRPPSS","RRRRRRRRRRRRRRSRRP","RRRRRRRRRRRRRRSRSP","RRRRRRRRRRRRRRSSPP","RRRRRRRRRRRRRPRPRP","RRRRRRRRRRRRRPPRSS","RRRRRRRRRRRRRPSRPS","RRRRRRRRRRRRRSPRSP","RRRRRRRRRRRRRSSRPP","RRRRRRRRRRRRPPPPPP","RRRRRRRRRRRRPPPSSS","RRRRRRRRRRRRSSSPPP","RRRRRRRRRRRPRRRRRS","RRRRRRRRRRRPRRPRRP","RRRRRRRRRRRPRPPRSP","RRRRRRRRRRRPRPPPRP","RRRRRRRRRRRPPRRRSS","RRRRRRRRRRRPPRPSSP","RRRRRRRRRRRPPPRSSS","RRRRRRRRRRRPSRRRPS","RRRRRRRRRRRPSRPPRP","RRRRRRRRRRRPSRPPPS","RRRRRRRRRRRPSSRPPS","RRRRRRRRRRRSRRRRRP","RRRRRRRRRRRSPPRSSP","RRRRRRRRRRRSSSRPPP","RRRRRRRRRRPRRPPRPS","RRRRRRRRRRPRPSPSRS","RRRRRRRRRRPPRRRRSS","RRRRRRRRRRPPRPPRPP","RRRRRRRRRRPPPRRPPP","RRRRRRRRRRPSRPPPPS","RRRRRRRRRRPSRPSRPS","RRRRRRRRRRPSSPSPPS","RRRRRRRRRRSRRSSRSP","RRRRRRRRRRSRSPSPRP","RRRRRRRRRRSPRSPRSP","RRRRRRRRRRSPRSSSSP","RRRRRRRRRRSPPSPSSP","RRRRRRRRRRSSRRRRPP","RRRRRRRRRPRRRSSSPP","RRRRRRRRRPRPPPSPRS","RRRRRRRRRPRPSPPSRP","RRRRRRRRRPRSPRSPRS","RRRRRRRRRPPPRRRSSS","RRRRRRRRRPPPPPPPPP","RRRRRRRRRPPSSPSRPS","RRRRRRRRRPPSSSRRRP","RRRRRRRRRSRPSRPSRP","RRRRRRRRRSPRSPSSPP","RRRRRRRRRSSSRRRPPP","RRRRRRRRPRRRRRRRRP","RRRRRRRRPRRRRRPRRS","RRRRRRRRPRRPRRSRRS","RRRRRRRRPRPRRRPRSS","RRRRRRRRPRPPSPSPPS","RRRRRRRRPRPSPPPSPS","RRRRRRRRPRSRRRRRPP","RRRRRRRRPRSPSSSPSS","RRRRRRRRPRSSPSPSSS","RRRRRRRRPPRPPSSPPS","RRRRRRRRPPPRRRRSSP","RRRRRRRRPPSSPRPPPS","RRRRRRRRPSRPSSSSPS","RRRRRRRRPSSRRRRPPP","RRRRRRRRSRRSRRPRRP","RRRRRRRRSRPSPPPSPP","RRRRRRRRSRSRRRSRPP","RRRRRRRPRRRPRPRRSS","RRRRRRRPRPRPRSRSRS","RRRRRRRPRPPPPPPPRP","RRRRRRRPPRRPRRSRPS","RRRRRRRPPPRRRRPSPS","RRRRRRRPPPRRRPRSSP","RRRRRRRPPPSRRRPSSS","RRRRRRRPSRRRRRRRPS","RRRRRRRPSRRSRRPRPP","RRRRRRRPSSRPRRRPPP","RRRRRRRSRRRSRSRRPP","RRRRRRRSRSRSRPRPRP","RRRRRRRSPRRRRRRRSP","RRRRRRRSPSPRRRRPPP","RRRRRRRSSSPRRRSPPP","RRRRRRPRPRPRPRRSSP","RRRRRRPRPRPSPRRSSS","RRRRRRPPRRSPPRRSSS","RRRRRRPPPRRRRRRPPP","RRRRRRPPPRRRPPPSSS","RRRRRRPPPPPPSSSSSS","RRRRRRPPPPPSPSSSSS","RRRRRRPPPPPSSPSSSS","RRRRRRPPPPPSSSPSSS","RRRRRRPPPPPSSSSSSP","RRRRRRPPPPSSSPPSSS","RRRRRRPPPSSSPPPSSS","RRRRRRPPSRPRRSRPSS","RRRRRRPPSPRRSRRSPS","RRRRRRPPSPPPSSSSSP","RRRRRRPPSPPSPSSPSS","RRRRRRPPSSSSPPPSSP","RRRRRRPSRRPSRRRPPP","RRRRRRPSPSPSPSPSPS","RRRRRRPSSRRPRPRPRP","RRRRRRPSSRRSRRPPSP","RRRRRRPSSRSRRPRPPS","RRRRRRPSSPPPSSSSPP","RRRRRRSSRRPSSRRPPP","RRRRRRSSSRRRSSSPPP","RRRRRRSSSSSSPPPPPP","RRRRRPRRRRRPRRRRRP","RRRRRPRRPPRPRRSSRP","RRRRRPRRSRRRRRPRRS","RRRRRPRRSSRPRRPPRP","RRRRRPRPRRRPRRRRPP","RRRRRPRPRPRPRSPSRS","RRRRRPRPRPPPRSRSSP","RRRRRPRPPRRPRSSRRP","RRRRRPRPPPPSSPSSSS","RRRRRPRPPPSPPSSSSS","RRRRRPRPPPSPSSSPSS","RRRRRPRPPPSPSSSSSP","RRRRRPRPPSPPSSSSSP","RRRRRPRPPSPSPSSSPS","RRRRRPRPPSPSSSPSPS","RRRRRPRPPSSPSPPSSS","RRRRRPRPSPPSPPSPRS","RRRRRPRSRSRSRPPPRP","RRRRRPRSRSSPRPRPPP","RRRRRPRSSRRPRPPRRP","RRRRRPPRRPPPSRRSSP","RRRRRPPRPPPSSSSPSS","RRRRRPPRPPSPPSSSSS","RRRRRPPRPPSSPPSSSS","RRRRRPPRPSPPRRSSSP","RRRRRPPRPSPPSPSSSS","RRRRRPPRSSPPSSSSPP","RRRRRPPRSSSPPSPSSP","RRRRRPPPRPSPSPSSSS","RRRRRPPPPPSSSRPSSS","RRRRRPPPPSPSRSPSSS","RRRRRPPPSRPSSSSPPS","RRRRRPPPSPPRSSPSSS","RRRRRPPSRPPSSSPSPS","RRRRRPPSPSSSPPRSPS","RRRRRPSRRSSPPRRPPP","RRRRRPSPRPPSSSSPSP","RRRRRPSSRRPSSRPPPP","RRRRRPSSPSPPSSSRPP","RRRRRSRRPRRRRRSRRP","RRRRRSRPSPPSPPSPRP","RRRRRSSSPRSSSPPPPP","RRRRRSSSPSRSPSPPPP","RRRRRSSSPSSRPPSPPP","RRRRPRRPPPSRRPPSSS","RRRRPRRSSSPRRPSPPP","RRRRPRPRPRPRPSPSRS","RRRRPRPSPSPSPSPSRS","RRRRPRSRPSPSPSPPSS","RRRRPPRRRRPPRRRRPP","RRRRPPRRSRPRRRPRPS","RRRRPPRPSRPSPPSSSS","RRRRPPRPSPPSSPSRSS","RRRRPPRSPRSPPSPSSS","RRRRPPRSPPSPSSPRSS","RRRRPPRSSRSPPSPSSP","RRRRPPRSSPPSSPSRPS","RRRRPPPRRRPPRRRPPP","RRRRPPPRRRPPPPRSSP","RRRRPPPRRSSPPPSSSS","RRRRPPPRSSPPRPSSSS","RRRRPPPPRSSPRPRSSP","RRRRPPPPRSSPPRSSSS","RRRRPPPSRSPPRSPSSS","RRRRPPPSPSSPRRSSSP","RRRRPPSRRPPSRRPPPP","RRRRPPSRRPPSSSPPSS","RRRRPSRRRRPSRRRRPS","RRRRPSRRPRPRRRSRPP","RRRRPSRPPRPSSSSPPS","RRRRPSRPPPPSRSSSPS","RRRRPSRPSRPSSSSPPP","RRRRPSRSSSPSRPPPPS","RRRRPSPRPPPSSRSSPS","RRRRPSPPSPRRSPSSPS","RRRRPSSRRPSSSSPPPP","RRRRPSSRPRPSSRPPPP","RRRRPSSRSRSPSPSPPP","RRRRPSSRSPSSRPPPPS","RRRRPSSRSSPSPRPPPS","RRRRPSSPSSRRPPSPPS","RRRRSRPRSPSPSPSSPP","RRRRSRSRSRSRSPSPRP","RRRRSRSPSPSPSPSPRP","RRRRSPRRRRSPRRRRSP","RRRRSPRPPRSPSSSPSP","RRRRSPRPPPSPRSSSSP","RRRRSPRSPSSPPSSRPP","RRRRSPRSSSSPRPPPSP","RRRRSPSSRRPSSSPPPP","RRRRSSRPSSPSPPSRPP","RRRRSSRSPRSPSSPPPP","RRRPRPRPSPRSPSRSRS","RRRPRPPSSPRSPPSSRS","RRRPRPSRPPPSSRPSSS","RRRPRPSRSSRPSPPSSP","RRRPRPSPRPSPSRPSSS","RRRPRPSPRSRPRSPSRS","RRRPRSRRRPRSRRRPRS","RRRPRSRPRPRSRRRPPS","RRRPRSRSRSRSPPSPRP","RRRPRSRSSSRPPSSPPP","RRRPRSPRPPPSSRSPSS","RRRPRSPRSPSSSPSPRP","RRRPRSSRSPSSPRPPPS","RRRPPRRRPPPRRPPPSS","RRRPPRRRSSPPPRRPPP","RRRPPRRPPPSSRPRPSS","RRRPPRRPPPSSSRPSSS","RRRPPRSRPPPSSPRSSS","RRRPPPRRRPPPRRRPPP","RRRPPPRRSPPRRRPPPS","RRRPPPSSSRRRPPPSSS","RRRPPSRRPPPRRRSPPP","RRRPPSRSRPRSRPRPSS","RRRPPSPSSRRRPPSPSS","RRRPPSSSPRRRPPSSSP","RRRPSRRSSSPRPSSPPP","RRRPSSRPRPRSRSRPPS","RRRSRPRRRSRPRRRSRP","RRRSRPRPRSRPRRRSPP","RRRSRPRSRSRSSPPPRP","RRRSRPPRPSPPSRSSSP","RRRSRPSRPSSPSPSPRP","RRRSRPSRSSSPPRPSPP","RRRSRSPRSSSPPRSPPP","RRRSPRRRSSSPPSSPPP","RRRSPRPRSSPRPRSPPP","RRRSPPRSRSRPRPRSSP","RRRSSPRPRSRPRSRSPP","RRRSSSPPPRRRSSSPPP","RRPRRPRRPRRPRRPRRP","RRPRRPRRPRPSRPSRPS","RRPRRPRRPPSSPSSPSS","RRPRRPRRPSPSSPSSPS","RRPRRPRRPSSPSSPSSP","RRPRRPRRSRSSRSSRSP","RRPRRPRRSPSSPSSPSP","RRPRRPRRSSPSSPSSPP","RRPRRPRPSRPSSPSSPS","RRPRRPRSPRSPPSSPSS","RRPRRPRSPSSPSSPSRP","RRPRRPRSSPSPRSSPSP","RRPRRPSRPSPSSRPSPS","RRPRPSRRPRPSRRPRPS","RRPRPSPRPSPSRSPSRS","RRPRPSPSPRRSPSPSRS","RRPRPSSPSRRPRPSSPS","RRPRSPPSSRRPRSPPSS","RRPPSSRRPPSSRRPPSS","RRPSRSRSPSPSPRPRPS","RRPSRSPSPRRSPSPRPS","RRPSPSRRPSPSRRPSPS","RRPSSPRRPSSPRRPSSP","RRSRSPRRSRSPRRSRSP","RRSPSPRRSPSPRRSPSP","RRSSPPRRSSPPRRSSPP","RPRPRPRPRPRPRPRPRP","RPRSPSRPRSPSRPRSPS","RPSRPSRPSRPSRPSRPS","RSPRSPRSPRSPRSPRSP"}
213123
100
1000
1
Returns: 960021683
5)
3
{"RRR", "RPS", "RPS"}
0
1
1
1
Returns: 5

We have 5 attuned sets: {0}, {1}, {2}, {0,1}, {0,2}.

6)
3
{"RRR", "RPS", "RSP"}
0
1
1
1
Returns: 7

This time we have 2 more since ("RPS", "RSP") are attuned: {0}, {1}, {2}, {0,1}, {0,2}, {1,2}, {0,1,2}.

7)
6
{"RRRR", "RRPP", "PSPS"}
123456789
1
1
1
Returns: 13

Input = {"RRRR", "RRPP", "PSPS", "RSRR", "PSSR", "PSRR"}.

8)
50
{"PPPPPPPPP"}
22222223
0
100
0
Returns: 898961330

All 2^50-1 non-empty subsets are good, so the answer is (2^50-1) % (10^9+7).

Submissions are judged against all 166 archived test cases, of which 9 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class RPSRobots with a public method int countGoodSet(int n, vector<string> r, int seed, int pR, int pP, int pS) · 166 test cases · 2 s / 256 MB per case

Submitting as anonymous