CF585D Lizard Era: Beginning [mid in middle]

板子。

// clang-format off
// powered by c++11
// by Isaunoya
#include<bits/stdc++.h>
#define rep(i,x,y) for(register int i=(x);i<=(y);++i)
#define Rep(i,x,y) for(register int i=(x);i>=(y);--i)
using namespace std;using db=double;using ll=long long;
using uint=unsigned int;using ull=unsigned long long;
using pii=pair<int,int>;
#define Tp template
#define fir first
#define sec second
Tp<class T>void cmax(T&x,const T&y){if(x<y)x=y;}Tp<class T>void cmin(T&x,const T&y){if(x>y)x=y;}
#define all(v) v.begin(),v.end()
#define sz(v) ((int)v.size())
#define pb emplace_back
Tp<class T>void sort(vector<T>&v){sort(all(v));}Tp<class T>void reverse(vector<T>&v){reverse(all(v));}
Tp<class T>void unique(vector<T>&v){sort(all(v)),v.erase(unique(all(v)),v.end());}inline void reverse(string&s){reverse(s.begin(),s.end());}
const int SZ=1<<23|233;
struct FILEIN{char qwq[SZ],*S=qwq,*T=qwq,ch;
#ifdef __WIN64
#define GETC getchar
#else
inline char GETC(){return(S==T)&&(T=(S=qwq)+fread(qwq,1,SZ,stdin),S==T)?EOF:*S++;}
#endif
inline FILEIN&operator>>(char&c){while(isspace(c=GETC()));return*this;}inline FILEIN&operator>>(string&s){s.clear();while(isspace(ch=GETC()));if(!~ch)return*this;s=ch;while(!isspace(ch=GETC())&&~ch)s+=ch;return*this;}
inline FILEIN&operator>>(char*str){char*cur=str;while(*cur)*cur++=0;cur=str;while(isspace(ch=GETC()));if(!~ch)return*this;*cur=ch;while(!isspace(ch=GETC())&&~ch)*++cur=ch;*++cur=0;return*this;}
Tp<class T>inline void read(T&x){bool f=0;while((ch=GETC())<48&&~ch)f^=(ch==45);x=~ch?(ch^48):0;while((ch=GETC())>47)x=x*10+(ch^48);x=f?-x:x;}
inline FILEIN&operator>>(int&x){return read(x),*this;}inline FILEIN&operator>>(ll&x){return read(x),*this;}inline FILEIN&operator>>(uint&x){return read(x),*this;}inline FILEIN&operator>>(ull&x){return read(x),*this;}
inline FILEIN&operator>>(double&x){read(x);bool f=x<0;x=f?-x:x;if(ch^'.')return*this;double d=0.1;while((ch=GETC())>47)x+=d*(ch^48),d*=.1;return x=f?-x:x,*this;}
}in;
struct FILEOUT{const static int LIMIT=1<<22;char quq[SZ],ST[233];int sz,O,pw[233];
FILEOUT(){set(7);rep(i,pw[0]=1,9)pw[i]=pw[i-1]*10;}~FILEOUT(){flush();}
inline void flush(){fwrite(quq,1,O,stdout),fflush(stdout),O=0;}
inline FILEOUT&operator<<(char c){return quq[O++]=c,*this;}inline FILEOUT&operator<<(string str){if(O>LIMIT)flush();for(char c:str)quq[O++]=c;return*this;}
inline FILEOUT&operator<<(char*str){if(O>LIMIT)flush();char*cur=str;while(*cur)quq[O++]=(*cur++);return*this;}
Tp<class T>void write(T x){if(O>LIMIT)flush();if(x<0){quq[O++]=45;x=-x;}do{ST[++sz]=x%10^48;x/=10;}while(x);while(sz)quq[O++]=ST[sz--];}
inline FILEOUT&operator<<(int x){return write(x),*this;}inline FILEOUT&operator<<(ll x){return write(x),*this;}inline FILEOUT&operator<<(uint x){return write(x),*this;}inline FILEOUT&operator<<(ull x){return write(x),*this;}
int len,lft,rig;void set(int l){len=l;}inline FILEOUT&operator<<(double x){bool f=x<0;x=f?-x:x,lft=x,rig=1.*(x-lft)*pw[len];return write(f?-lft:lft),quq[O++]='.',write(rig),*this;}
}out;
#define int long long
struct Math{
vector<int>fac,inv;int mod;
void set(int n,int Mod){fac.resize(n+1),inv.resize(n+1),mod=Mod;rep(i,fac[0]=1,n)fac[i]=fac[i-1]*i%mod;inv[n]=qpow(fac[n],mod-2);Rep(i,n-1,0)inv[i]=inv[i+1]*(i+1)%mod;}
int qpow(int x,int y){int ans=1;for(;y;y>>=1,x=x*x%mod)if(y&1)ans=ans*x%mod;return ans;}int C(int n,int m){if(n<0||m<0||n<m)return 0;return fac[n]*inv[m]%mod*inv[n-m]%mod;}
int gcd(int x,int y){return!y?x:gcd(y,x%y);}int lcm(int x,int y){return x*y/gcd(x,y);}
}math;
// clang-format on

int n , mid;
const int maxn = 30;
int a[maxn], b[maxn], c[maxn];

map < pii , pii > mp;

void dfs(int x , int y , int z , int dep , int msk) {
	if(dep > mid) {
		pii fuck = { x - z , x - y } ;
		if(mp.count(fuck)) {
			if(mp[fuck].fir < x) {
				mp[fuck] = { x , msk };
			}
		}
		else mp[fuck] = { x , msk };
		return;
	}
	dfs(x + a[dep], y + b[dep], z, dep + 1, msk * 3);
	dfs(x + a[dep], y, z + c[dep], dep + 1, msk * 3 + 1);
	dfs(x, y + b[dep], z + c[dep], dep + 1, msk * 3 + 2);
}

int ans = -1e18, msk1, msk2;
void dfs2(int x , int y , int z , int dep , int msk) {
	if(dep <= mid) {
		pii fuck = { z - x , y - x } ;
		if(mp.count(fuck)) {
			if(mp[fuck].fir + x > ans) {
				ans = mp[fuck].fir + x;
				msk1 = mp[fuck].sec;
				msk2 = msk;
			}
		}
		return ;
	}	
	dfs2(x + a[dep], y + b[dep], z, dep - 1, msk * 3);
	dfs2(x + a[dep], y, z + c[dep], dep - 1, msk * 3 + 1);
	dfs2(x, y + b[dep], z + c[dep], dep - 1, msk * 3 + 2);
}
string s[4];
signed main(){
	//code begin.
	s[0] = "LM", s[1] = "LW", s[2] = "MW";
	in >> n;
	rep(i , 1 , n) in >> a[i] >> b[i] >> c[i];
	mid = n + 1 >> 1; 
	dfs(0 , 0 , 0 , 1 , 1);
	dfs2(0 , 0 , 0 , n , 1);
	if(!msk1 && !msk2) {
		out << "Impossible" << '
';
		return 0;
	}
	stack < int > stk;
	while(msk1 ^ 1) {
		stk.push(msk1 % 3);
		msk1 /= 3;
	}
	while(stk.size()) {
		out << s[stk.top()] << '
';
		stk.pop();
	}
	while(msk2 ^ 1) {
		out << s[msk2 % 3] << '
';
		msk2 /= 3;
	}
	return 0;
	//code end.
}