// Judges with GCC >= 12 only needs Ofast
// #pragma GCC optimize("O3,no-stack-protector,fast-math,unroll-loops,tree-vectorize")
// MLE optimization
// #pragma GCC optimize("conserve-stack")
// Old judges
// #pragma GCC target("sse4.2,popcnt,lzcnt,abm,mmx,fma,bmi,bmi2")
// New judges. Test with assert(__builtin_cpu_supports("avx2"));
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")
// Atcoder
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma")
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
- insert(x),erase(x)
- find_by_order(k): return iterator to the k-th smallest element
- order_of_key(x): the number of elements that are strictly smaller
*/
#include<bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
uniform_real_distribution<> pp(0.0,1.0);
#define int long long
#define ld long double
#define pii pair<int,int>
#define piii pair<int,pii>
#define mpp make_pair
#define fi first
#define se second
const int inf=1e18;
const int mod=998244353;
const int maxn=40;
const int bl=650;
const int maxs=655;
const int maxm=200005;
const int maxq=1000005;
const int maxl=25;
const int maxa=1000000;
const int root=3;
int power(int a,int n){
    int res=1;
    while(n){
        if(n&1) res=res*a%mod;
        a=a*a%mod;n>>=1;
    }
    return res;
}
const int iroot=power(3,mod-2);
const int base=101;

int n;

//Brackets
int C2[2*maxn][2*maxn];
void buildC(){
    C2[0][0]=1;
    for(int i=1;i<=2*n;i++){
        for(int j=0;j<=i;j++){
            if(j) C2[i][j]=C2[i-1][j+1]+C2[i-1][j-1];
            else C2[i][j]=C2[i-1][j+1];
        }
    }
}
int brackets_to_num(string s){
    int cur=0,total=0;
    for(int i=0;i<2*n;i++){
        if(s[i]=='('){
            if(cur) total+=C2[2*n-i-1][cur-1];
            cur++;
        }
        else cur--;
    }
    return total;
}
string num_to_brackets(int total){
    int cur=0;
    string s;
    for(int i=0;i<2*n;i++){
        if(!cur || total>=C2[2*n-i-1][cur-1]){
            if(cur) total-=C2[2*n-i-1][cur-1];
            s+='(';
            cur++;
        }
        else{
            s+=')';
            cur--;
        }
    }
    return s;
}
//Triang
string triang_to_brackets(vector<tuple<int,int,int>> T){
    string res;
    function<void(int,int)> dnc = [&](int x,int y){
        if(y<=x+1) return;
        int mid=-1;
        for(auto [p,q,r]:T) if(p==x && r==y) mid=q;
        res+='(';
        dnc(x,mid);
        res+=')';
        dnc(mid,y);
    };
    dnc(1,n+2);
    return res;
}

vector<tuple<int,int,int>> brackets_to_triang(string s){
    vector<tuple<int,int,int>> T;
    function<void(int,int,int,int)> dnc = [&](int x,int y,int l,int r){
        if(l>r) return;
        int cnt=0,cur=0,i=0;
        for(i=l;i<=r;i++){
            if(s[i]=='(') cnt++,cur++;
            else cur--;
            if(!cur) break;
        }
        T.push_back({x,x+cnt,y});
        dnc(x,x+cnt,l+1,i-1);
        dnc(x+cnt,y,i+1,r);
    };
    dnc(1,n+2,0,(int)s.size()-1);
    sort(T.begin(),T.end());
    return T;
}

void print_triang(int total){
    string x=num_to_brackets(total);
    vector<tuple<int,int,int>> tri=brackets_to_triang(x);
    cout << "triang\n";
    for(auto [p,q,r]:tri) cout << p << ' ' << q << ' ' << r << '\n';
}



//Perm

string perm_to_brackets(vector<int> p){
    vector<int> cnt(n,0);
    queue<int> q;
    string s;
    int Max=0,pos=0;
    for(int a:p){
        if(a>Max){
            Max=a,s+='(';
            q.push(a);
        }
        else s+="()";
        cnt[a-1]++;
        while(pos<n && cnt[pos]) pos++;
        while(!q.empty() && q.front()<=pos) s+=')',q.pop();
    }
    return s;
}
vector<int> brackets_to_perm(string s){
    vector<int> p(n,-1);
    deque<int> dq;
    int cur=1,pos=0;
    for(int i=0;i<2*n;i++){
        if(s[i]=='(') dq.push_back(pos++);
        else{
            if(s[i-1]=='('){
                p[dq.back()]=cur++;
                dq.pop_back();
            }
            else{
                p[dq.front()]=cur++;
                dq.pop_front();
            }
        }
    }
    return p;
}
void print_perm(int total){
    string x=num_to_brackets(total);
    vector<int> p=brackets_to_perm(x);
    cout << "perm\n";
    for(int a:p) cout << a << ' ';
    cout << '\n';
}


//Poly

string poly_to_brackets(vector<vector<char>> c){
    string lt,rt;
    int x=(int)c.size()-1,y=0;
    for(int i=1;i<n;i++){
        if(x && c[x-1][y]=='#'){
            x--;
            lt+='(';
        }
        else{
            y++;
            lt+=')';
        }
    }
    x=(int)c.size()-1;y=0;
    for(int i=1;i<n;i++){
        if(y<(int)c[0].size()-1 && c[x][y+1]=='#'){
            y++;
            rt+='(';
        }
        else{
            x--;
            rt+=')';
        }
    }
    string s;s+='(';
    for(int i=0;i<n-1;i++){
        s+=rt[i];
        s+=lt[i];
    }
    s+=')';
    return s;
}
vector<vector<char>> brackets_to_poly(string s){
    string lt,rt;
    for(int i=1;i<2*n-1;i++){
        if(i&1) rt+=s[i];
        else lt+=s[i];
    }
    int h=1,w=1;
    for(char c:lt){
        if(c=='(') h++;
        else w++;
    }
    vector<vector<char>> c(h,vector<char>(w,'.'));
    vector<int> Max(h,-1),Min(h,w+1);
    int x=h-1,y=0;
    Max[x]=Min[x]=y;
    for(int i=0;i<n-1;i++){
        if(lt[i]=='(') x--;
        else y++;
        Max[x]=max(Max[x],y);
        Min[x]=min(Min[x],y);
    }
    x=h-1;y=0;
    for(int i=0;i<n-1;i++){
        if(rt[i]=='(') y++;
        else x--;
        Max[x]=max(Max[x],y);
        Min[x]=min(Min[x],y);
    }
    for(int i=0;i<h;i++){
        for(int j=Min[i];j<=Max[i];j++) c[i][j]='#';
    }
    return c;
}
void print_poly(int total){
    string x=num_to_brackets(total);
    vector<vector<char>> c=brackets_to_poly(x);
    cout << "poly\n";
    cout << (int)c.size() << ' ' << (int)c[0].size() << '\n';
    for(int i=0;i<(int)c.size();i++){
        for(int j=0;j<(int)c[i].size();j++) cout << c[i][j];
        cout << '\n';
    }
}


void solve(){
    string type;cin >> type;
    if(type=="poly"){
        int h,w;cin >> h >> w;
        vector<vector<char>> c(h,vector<char>(w));
        for(int i=0;i<h;i++) for(int j=0;j<w;j++) cin >> c[i][j];
        string x=poly_to_brackets(c);
        int total=brackets_to_num(x);
        if(total&1) print_triang(total-1);
        else print_perm(total+1);
    }
    else if(type=="perm"){
        vector<int> p(n);
        for(int i=0;i<n;i++) cin >> p[i];
        string x=perm_to_brackets(p);
        int total=brackets_to_num(x);
        if(total&1) print_poly(total-1);
        else print_triang(total+1);
    }
    else{
        vector<tuple<int,int,int>> T(n);
        for(int i=0;i<n;i++){
            int x,y,z;cin >> x >> y >> z;
            T[i]={x,y,z};
        }
        string x=triang_to_brackets(T);
        int total=brackets_to_num(x);
        if(total&1) print_perm(total-1);
        else print_poly(total+1);
    }
}
signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);cout.tie(NULL);
    int test=1;cin >> n >> test;
    cout << n << ' ' << test << '\n';
    buildC();
    while(test--) solve();
}