codeforces - 100819 V

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i = a;i <= b;++ i)
#define per(i,a,b) for(int i = a;i >= b;-- i)
#define mem(a,b) memset((a),(b),sizeof((a)))
#define FIN freopen("in.txt","r",stdin)
#define IO ios_base::sync_with_stdio(0),cin.tie(0)
#define pb push_back
typedef long long LL;
typedef pair<int, int> PIR;
const int N = 1e+5;

int n, use, stu[N];
bool vis[N];
vector <int> G[N];
struct Node{
    LL x, y;
    LL r;
}node[N];

bool judge(int i, int j){
    LL xi = node[i].x-node[j].x, yi = node[i].y-node[j].y;
    LL ri = node[i].r+node[j].r;
    return (xi*xi+yi*yi) == ri*ri;
}
void Test(){
    cout << "-----------TEST----------" << endl;
    rep(i, 1, n){
        cout << i << ": ";
        rep(j, 0, (int)G[i].size()-1)   cout << G[i][j] << " ";
        cout << endl;
    }
    cout << endl;
}

void bfs(){
    queue <PIR> Q;
    mem(stu, -1);
    mem(vis, false);
    use = 1;
    Q.push(PIR(1, 0));
    stu[1] = 0;
    vis[1] = true;
    while(!Q.empty()){
        PIR pir = Q.front(); Q.pop();
        int u = pir.first, st = pir.second;
        if(u == n){
            if(st^0 == 1)   cout << "-";
            LL gcd = __gcd(node[n].r, node[1].r);
            cout << node[1].r/gcd << ":" << node[n].r/gcd << endl;
            return ;
        }
        rep(i, 0, (int)G[u].size()-1){
            int v = G[u][i];
            if(stu[v] != -1 && stu[v]^st == 0){
                cout << "The input gear cannot move." << endl;
                return ;
            }

            if(vis[v])  continue;
            if(stu[v] == -1 || (stu[v] != -1 && stu[v]^st == 1)){
                stu[v] = st^1;
                vis[v] = true;
                Q.push(PIR(v, st^1));
            }
        }
    }
    cout << "The input gear is not connected to the output gear." << endl;
    return ;
}
int main()
{IO;
    //FIN;
    cin >> n;
    rep(i, 1, n)    cin >> node[i].x >> node[i].y >> node[i].r;
    rep(i, 1, n)    rep(j, i+1, n)  if(judge(i, j)) { G[i].pb(j); G[j].pb(i); }
    //Test();
    bfs();
    return 0;
}