Problem:
Score : 600 points

Problem Statement

We have 3N cards arranged in a row from left to right, where each card has an integer between 1 and N (inclusive) written on it. The integer written on the i-th card from the left is A_i.

You will do the following operation N-1 times:

Rearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain 1 point.

After these N-1 operations, if the integers written on the remaining three cards are all equal, you will gain 1 additional point.

Find the maximum number of points you can gain.

Constraints

1 \leq N \leq 2000

1 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_{3N}

Output

Print the maximum number of points you can gain.

Sample Input 1

2
1 2 1 2 2 1

Sample Output 1

2

Let us rearrange the five leftmost cards so that the integers written on the six cards will be 2\ 2\ 2\ 1\ 1\ 1 from left to right.

Then, remove the three leftmost cards, all of which have the same integer 2, gaining 1 point.

Now, the integers written on the remaining cards are 1\ 1\ 1.

Since these three cards have the same integer 1, we gain 1 more point.

In this way, we can gain 2 points - which is the maximum possible.

Sample Input 2

3
1 1 2 2 3 3 3 2 1

Sample Output 2

1

Sample Input 3

3
1 1 2 2 2 3 3 3 1

Sample Output 3

3

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

"use strict";
var input=require("fs").readFileSync("/dev/stdin","utf8");
var cin=input.split(/ |\n/),cid=0;
function next(){return +cin[cid++];}
function nextstr(){return cin[cid++];}
function nextbig(){return BigInt(cin[cid++]);}
function nexts(n,a){return a?cin.slice(cid,cid+=n):cin.slice(cid,cid+=n).map(a=>+a);}
function nextm(h,w,a){var r=[],i=0;if(a)for(;i<h;i++)r.push(cin.slice(cid,cid+=w));else for(;i<h;i++)r.push(cin.slice(cid,cid+=w).map(a=>+a));return r;}
function xArray(v){var a=arguments,l=a.length,r="Array(a["+--l+"]).fill().map(x=>{return "+v+";})";while(--l)r="Array(a["+l+"]).fill().map(x=>"+r+")";return eval(r);}

var myOut = main();
if(myOut !== undefined)console.log(String(myOut));

function main(){
  var n = next();
  var dp = xArray(-1,n,n), mx = 0, add = 0;
  var a = nexts(2).sort((a,b)=>a-b).map(a=>a-1);
  var q = [];
  var map = xArray(0,n);
  dp[a[0]][a[1]] = 0;
  map[a[0]]++, map[a[1]]++;
  for(var i = 1; i < n; i++){
    a = nexts(3).sort((a,b)=>a-b).map(a=>a-1);
    if(a[0] === a[2]){
      add++;
      continue;
    }
    q = [];
    solve(a[0],a[0],a[1],a[2]);
    if(a[0] !== a[1])solve(a[1],a[1],a[0],a[2]);
    else{
      for(var j = 0; j < a[0]; j++){
        solve(j,a[0],j,a[2]);
      }
      for(var j = a[0]+1; j < a[2]; j++){
        solve(a[0],j,j,a[2]);
      }
      for(var j = a[2]; j < n; j++){
        solve(a[0],j,a[2],j);
      }
    }
    if(a[1] !== a[2])solve(a[2],a[2],a[0],a[1]);
    else{
      for(var j = 0; j < a[0]; j++){
        solve(j,a[1],j,a[0]);
      }
      for(var j = a[0]; j < a[2]; j++){
        solve(j,a[2],a[0],j);
      }
      for(var j = a[2]+1; j < n; j++){
        solve(a[2],j,a[0],j);
      }
    }
    while(q.length){
      var w = q.pop(), v = q.pop(), u = q.pop();
      dp[u][v] = Math.max(dp[u][v], w);
    }
    for(var j = 0; j < 3; j++){
      var t = a[j];
      if(map[t] === 1)map[t] = 2, dp[t][t] = Math.max(0,dp[t][t]);
      else if(map[t] === 0){
        map[t] = 1;
        for(var k = 0; k < t; k++){
          if(map[k] === 0)continue;
          dp[k][t] = Math.max(0,dp[k][t]);
        }
        for(var k = t+1; k < n; k++){
          if(map[k] === 0)continue;
          dp[t][k] = Math.max(0,dp[t][k]);
        }
      }
    }
  }
  a = next()-1;
  solve(a,a,a,a);
  return mx+add;
  function solve(t,u,v,w){
    var x = Math.max(dp[v][w], dp[t][u]+1);
    q.push(v,w,x);
    mx = Math.max(mx,x);
  }
}