/****************************************************************************************************
經典DP,LIS,最長上升子序列
****************************************************************************************************/
#include <iostream>
#include <iomanip>
#include <functional>
#include <algorithm>
#include <complex>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <sstream>
#include <utility>
#include <bitset>
#include <cctype>
#include <cstdio>
#include <limits>
#include <memory>
#include <string>
#include <vector>
#include <cmath>
#include <ctime>
#include <queue>
#include <stack>
#include <list>
#include <map>
#include <set>
using namespace std;
#define LOWBIT(x) ( (x) & ( (x) ^ ( (x) - 1 ) ) )
#define CLR(x, k) memset((x), (k), sizeof(x))
#define CPY(t, s) memcpy((t), (s), sizeof(s))
#define SC(t, s) static_cast<t>(s)
#define LEN(s) static_cast<int>( strlen((s)) )
#define SZ(s) static_cast<int>( (s).size() )
typedef double LF;
//typedef long long LL; //GNU C++
//typedef unsigned long long ULL;
typedef __int64 LL; //Visual C++ 2010
typedef unsigned __int64 ULL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<double, double> PDD;
typedef map<int, int>::iterator MI;
typedef vector<int>::iterator VI;
typedef list<int>::iterator LI;
typedef set<int>::iterator SI;
template <typename T>
T sqa(const T &x)
{
return x * x;
}
template <typename T>
T gcd(T a, T b)
{
if (!a || !b)
{
return max(a, b);
}
T t;
while (t = a % b)
{
a = b;
b = t;
}
return b;
}
template <typename T>
T ext_gcd(T a, T b, T &x, T &y)
{
if (!b)
{
x = 1;
y = 0;
return a;
}
T d = ext_gcd(b, a % b, x, y);
T t = x;
x = y;
y = t - a / b * y;
return d;
}
template <typename T>
T invmod(T a, T p)
{
LL inv, y;
ext_gcd(a, p, inv, y);
inv < 0 ? inv += p : 0;
return inv;
}
const int INF_INT = 0x3f3f3f3f;
const LL INF_LL = 0x7fffffffffffffffLL; //15f
const double oo = 10e9;
const double eps = 10e-7;
const double PI = acos(-1.0);
#define ONLINE_JUDGE
const int MAXN = 504;
const int loop[][3] = {{0, 1, 2}, {0, 2, 1}, {2, 1, 0}};
int n, cube[MAXN][3];
int dp[MAXN];
struct Node
{
int x, y, z;
int s;
bool operator < (const Node &rhs) const
{
return x < rhs.x && y < rhs.y || x < rhs.y && y < rhs.x;
}
bool operator > (const Node &rhs) const
{
return x > rhs.x && y > rhs.y || x > rhs.y && y > rhs.x;
}
}node[MAXN], tmp[MAXN];
bool inline nodeCmp(const Node &na, const Node &nb)
{
return na.s < nb.s;
}
void ace()
{
int cas = 1;
int ncnt;
while (cin >> n, n)
{
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < 3; ++j)
{
cin >> cube[i][j];
}
}
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < 3; ++j) //因爲立方體是無限的,但是x,y相同的立方體只可能出現一次
{
int k = i * 3 + j;
node[k].x = cube[i][ loop[j][0] ];
node[k].y = cube[i][ loop[j][1] ];
node[k].z = cube[i][ loop[j][2] ];
node[k].s = node[k].x * node[k].y;
}
}
n *= 3;
sort(node, node + n, nodeCmp); //對面積排序,儘量使小面積的在前面
ncnt = 0;
CLR(dp, 0);
dp[0] = node[0].z; //dp數組記錄在當前第i個立方體放入後,以第i個立方體爲底的高度
for (int i = 1; i < n; ++i)
{
int buf = 0;
for (int j = 0; j < i; ++j)
{
if (node[i] > node[j] && buf < dp[j]) //顯然應該找之前最高的,因爲只要保證node[i] > node[j]
{ //那麼i之前的狀態對於i來說是無關的
buf = dp[j];
}
}
dp[i] = buf + node[i].z;
}
int res = 0;
for (int i = 0; i < n; ++i)
{
res = max(res, dp[i]);
}
printf("Case %d: maximum height = %d\n", cas++, res);
}
return ;
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
#endif
ace();
return 0;
}
HDU 1069 DP
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