#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int, int> pi;
#define debug(x) cerr << #x << ": " << x << endl
#define debug2(x, y) debug(x), debug(y)
#define repn(i, a, b) for(int i = (int)(a); i < (int)(b); i++)
#define rep(i, a) for(int i = 0; i < (int)(a); i++)
#define all(v) v.begin(), v.end()
#define mp make_pair
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define fi first
#define se second
#define sq(x) ((x) * (x))
const int mxN = 1e5 + 5;
template<class T> T gcd(T a, T b){ return ((b == 0) ? a : gcd(b, a % b)); }
struct DSU{
int S;
struct node{
int parent; ll sum;
};
vector<node> dsu;
DSU(int n){
S = n;
rep(i, n){
node tmp;
tmp.parent = i; tmp.sum = 1;
dsu.pb(tmp);
}
}
int root(int u){
if(dsu[u].parent == u) return u;
dsu[u].parent = root(dsu[u].parent);
return dsu[u].parent;
}
void merge(int u, int v){
u = root(u); v = root(v);
if(u == v) return;
if(getsum(u) < getsum(v)) swap(u, v);
dsu[v].parent = u;
dsu[u].sum += dsu[v].sum;
}
bool sameset(int u, int v){
if(root(u) == root(v)) return true;
return false;
}
ll getsum(int u){
return dsu[root(u)].sum;
}
} dsuB(mxN), dsuR(mxN);
int n;
int a, b;
vi g[mxN], g1[mxN]; //g is blue, g1 is red
void end(int f){
if(!f) cout << "Magenta" << endl;
else if(f == 1) cout << "Paula" << endl;
else cout << "Marin" << endl;
exit(0);
}
int tmF[mxN], dist[mxN];
int vis[mxN], vis1[mxN];
set<int> aset, bset;
int d1 = -1, d2 = -1;
void dfs(int cur, int prev, int d){
vis[cur] = 1;
if(bset.find(cur) != bset.end()) d1 = d;
for(int x : g[cur]) if(x != prev && !vis[x]) dfs(x, cur, d + 1);
}
void dfs1(int cur, int prev, int d){
vis1[cur] = 1;
if(aset.find(cur) != aset.end()) d2 = d;
for(int x : g1[cur]) if(x != prev && !vis1[x]) dfs1(x, cur, d + 1);
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
//freopen("input.in", "r", stdin);
//freopen("output.out", "w", stdout);
cin >> n;
cin >> a >> b;
a--, b--;
rep(i, n - 1){
int a, b;
string s;
cin >> a >> b >> s;
a--, b--;
if(s[0] == 'p' || s[0] == 'm'){
g[a].pb(b);
g[b].pb(a);
}
if(s[0] == 'c' || s[0] == 'm'){
g1[a].pb(b);
g1[b].pb(a);
}
}
if(!g[a].size() || ((int)g[a].size() == 1 && g[a][0] == b)) end(2);
if(!g1[b].size()) end(1);
for(int x : g[a]) aset.insert(x);
for(int x : g1[a]) aset.insert(x);
for(int x : g[b]) bset.insert(x);
for(int x : g1[b]) bset.insert(x);
dfs(a, -1, 0);
dfs1(b, -1, 0);
rep(i, n) if(!vis1[i]){
for(int x : g[i]) if(!vis1[x]) dsuB.merge(i, x);
}
rep(i, n) if(!vis[i]){
for(int x : g1[i]) if(!vis[x]) dsuR.merge(i, x);
}
if(dsuB.getsum(a) > 1 && dsuR.getsum(b) > 1) end(0);
memset(tmF, 0, sizeof(tmF));
set<pair<int, pi>> q;
tmF[a] = 1;
tmF[b] = 2;
q.insert(mp(0, mp(a, 1)));
q.insert(mp(1, mp(b, 2)));
rep(i, n) dist[i] = 1e9;
dist[a] = 0, dist[b] = 1;
while(!q.empty()){
pair<int, pi> cur = *q.begin();
q.erase(q.begin());
if(cur.se.se == 1){
for(int x : g[cur.se.fi]) if(!tmF[x] || dist[cur.se.fi] + 2 < dist[x]){
q.erase(mp(dist[x], mp(x, tmF[x])));
tmF[x] = cur.se.se;
dist[x] = 2 + dist[cur.se.fi];
q.insert(mp(dist[x], mp(x, tmF[x])));
}
}
else{
for(int x : g1[cur.se.fi]) if(!tmF[x] || dist[cur.se.fi] + 2 < dist[x]){
q.erase(mp(dist[x], mp(x, tmF[x])));
tmF[x] = cur.se.se;
dist[x] = 2 + dist[cur.se.fi];
q.insert(mp(dist[x], mp(x, tmF[x])));
}
}
}
int f = 0, f1 = 0;
rep(i, n) if(dsuB.getsum(i) > 1 && tmF[i] == 1) f = 1;
rep(i, n) if(dsuR.getsum(i) > 1 && tmF[i] == 2) f1 = 1;
if(f && f1) end(0); //both can hide
if(!f && !f1){
if(d1 % 2 == 0) end(1);
else end(2);
else end(0);
}
if(!f && f1){
//second maybe win?
if(d2 & 1) end(2);
else end(0);
}
if(f && !f1){
//first maybe win?
if(d1 % 2 == 0) end(1);
else end(0);
}
return 0;
}
/*
Things to look out for:
- Integer overflows
- Make sure that max is large enough (2e9, 4e18)
- Special cases
Be careful!
*/
Compilation message
Main.cpp: In function 'int main()':
Main.cpp:158:3: error: expected '}' before 'else'
158 | else end(0);
| ^~~~
Main.cpp:155:15: note: to match this '{'
155 | if(!f && !f1){
| ^
Main.cpp: At global scope:
Main.cpp:160:2: error: expected unqualified-id before 'if'
160 | if(!f && f1){
| ^~
Main.cpp:165:2: error: expected unqualified-id before 'if'
165 | if(f && !f1){
| ^~
Main.cpp:170:2: error: expected unqualified-id before 'return'
170 | return 0;
| ^~~~~~
Main.cpp:171:1: error: expected declaration before '}' token
171 | }
| ^
