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: Accepted)

"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(-1e9,n+1,n+1), add = 0;
  var a = nexts(2).sort((a,b)=>a-b), q;
  dp[0][0] = dp[0][a[0]] = dp[0][a[1]] = dp[a[0]][a[1]] = 0;
  for(var i = 1; i < n; i++){
    a = nexts(3).sort((a,b)=>a-b);
    solve(...a);
  }
  a = next();
  return Math.max(dp[0][0],dp[a][a]+1) + add;
  function solve(u,v,w){
    if(u === w)return add++;
    q = [];
    solve1(u);
    if(u<v)solve1(v);
    if(v<w)solve1(w);
    solve2(u,v);
    if(v<w)solve2(u,w);
    if(u<v)solve2(v,w);
    solve3(u,v,w);
    while(q.length){
      var x = q.pop(), y = q.pop(), z = q.pop();
      if(dp[x][y] < z)dp[x][y] = z;
    }
  }
  function solve1(u){
    f1(0,0,u,u);
    for(var i = 0; i < u; i++){
      f0(i,u,0,i);
    }
    for(var i = u; i <= n; i++){
      f0(u,i,0,i);
    }
  }
  function solve2(u,v){
    f0(u,v,0,0);
    f1(0,v,u,u);
    if(u < v){
      f1(0,u,v,v);
    }else{//u=v
      for(var i = 0; i < u; i++){
        f1(0,i,i,u);
      }
      for(var i = u; i <= n; i++){
        f1(0,i,u,i);
      }
    }
  }
  function solve3(u,v,w){
    f1(v,w,u,u);
    if(u < v){
      f1(u,w,v,v);
      if(v < w){
        f1(u,v,w,w);
      }else{//v=w
        for(var i = 0; i < u; i++){
          f1(i,u,i,w);
        }
        for(var i = u; i < w; i++){
          f1(u,i,i,w);
        }
        for(var i = w; i <= n; i++){
          f1(u,i,w,i);
        }
      }
    }else{//u=v
      f1(u,u,w,w);
      for(var i = 0; i < u; i++){
        f1(i,w,i,u);
      }
      for(var i = u; i < w; i++){
        f1(i,w,u,i);
      }
      for(var i = w; i <= n; i++){
        f1(w,i,u,i);
      }
    }
  }
  function f0(a,b,c,d){
    if(dp[a][b] < dp[c][d])q.push(dp[c][d],b,a);
  }
  function f1(a,b,c,d){
    if(dp[a][b] < dp[c][d]+1)q.push(dp[c][d]+1,b,a);
  }
}