#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <string>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <algorithm>
#include <sstream>
#include <iostream>
#include <cassert>
using namespace std;
typedef long long ll;

#define REP(i,n) for (ll i=0; i<(ll)(n); ++i)
#define FOR(i,k,n) for (ll i=(k); i<(ll)(n); ++i)
#define FOREQ(i,k,n) for (ll i=(k); i<=(ll)(n); ++i)
#define FORIT(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define SZ(v) (ll)((v).size())
#define MEMSET(v,h) memset((v),(h),sizeof(v))

typedef ll Weight;
struct Edge {
  ll src;
  ll dest;
  Weight weight;
  Edge() {;}
  Edge(ll src, ll dest, Weight weight) : src(src), dest(dest), weight(weight) {;}
};

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
typedef vector<Weight> Array;
typedef vector<Array> Matrix;

/*
   void PrllMatrix(const Matrix &mat) {
   REP(y, h) {
   REP(x, w) {
   prllf("%d ", mat[y][x]);
   }
   puts("");
   }
   }
   */

ll MaxFlow(const Graph &g, ll s, ll t, Matrix &flow) {
  const ll n = g.size();
  flow = Matrix(n, Array(n, 0));
  Matrix capacity(n, Array(n, 0));
  REP(i, n) {
    FORIT(it, g[i]) {
      capacity[it->src][it->dest] += it->weight;
    }
  }
  ll ret = 0;
  vector<ll> parent(n);
  while (true) {
    fill(parent.begin(), parent.end(), -1);
    queue<Edge> que;
    que.push(Edge(s, s, 0));
    while (!que.empty()) {
      Edge node = que.front();
      que.pop();
      if (parent[node.dest] != -1) { continue; }
      parent[node.dest] = node.src;
      if (node.dest == t) { break; }
      ll from = node.dest;
      FORIT(it, g[from]) {
        ll to = it->dest;
        if (capacity[from][to] == 0 || parent[to] != -1) { continue; }
        que.push(Edge(from, to, 0));
      }
    }
    if (parent[t] == -1) { break; }
    Weight f = 1 << 30;
    ll from = parent[t];
    ll to = t;
    while (from != to) {
      f = min(f, capacity[from][to]) ;
      from = parent[from];
      to = parent[to];
    }
    from = parent[t];
    to = t;
    while (from != to) {
      capacity[from][to] -= f;
      capacity[to][from] += f;
      flow[from][to] += f;
      flow[to][from] -= f;
      from = parent[from];
      to = parent[to];
    }
    ret += f;
  }
  return ret;
}

void AddEdge(Graph &g, ll from, ll to, ll weight) {
  if (weight == 0) { return; }
  g[from].push_back(Edge(from, to, weight));
  g[to].push_back(Edge(to, from, weight));
  cout << from << " " << to << " " << weight << endl;
}

//====================================

ll Getll(const char *str, ll &index) {
  ll ret = 1;
  if (isdigit(str[index])) {
    ret = atoi(str + index);
    while (isdigit(str[index])) { index++; }
  }
  return ret;
}

vector<ll> Parse(const char *str) {
  vector<ll> ret(52, 0);
  //ll len = strlen(str);
  ll index = 0;
  while (str[index]) {
    ll a = Getll(str, index);;
    ll degree = 0;
    if (str[index] == 'x') {
      degree = 1;
      index++;
      if (str[index] == '^') {
        index++;
        degree = Getll(str, index);
      }
    }
    if (str[index] == '+') { index++; }
    ret[degree] = a;
  }
  return ret;
}

void PrintAns(vector<ll> &ans) {
  bool first = true;
  for (ll i = 51; i >= 0; i--) {
    if (ans[i] == 0) { continue; }
    if (!first) { printf("+"); }
    first = false;
    if (i == 0) {
      printf("%lld", ans[i]);
    } else if (i >= 1) {
      if (ans[i] >= 2) {
        printf("%lld", ans[i]);
      }
      printf("x");
      if (i >= 2) {
        printf("^%lld", i);
      }
    }
  }
  if (first) {
    printf("0");
  }
  puts("");
}


const ll INF = 1 << 28;
ll n, m;
//ll u[1000];
//ll v[1000];
vector<ll> poly[60][60];
//vector<ll> poly[1000];
char str[6666];

int main() {
  while (scanf("%lld %lld", &n, &m), n|m) {
    REP(y, 60) REP(x, 60) { poly[y][x] = vector<ll>(52, 0); }
    REP(i, m) {
      ll u, v;
      scanf("%lld %lld %s", &u, &v, str);
      u--; v--;
      vector<ll> p = Parse(str);
      REP(j, 51) {
        poly[u][v][j] += p[j];
        poly[v][u][j] += p[j];
      }
    }
    vector<ll> ans(52, 0);
    for (ll i = 51; i >= 0; i--) {
      Graph g(n);
      REP(y, n) {
        REP(x, n) {
          if (poly[y][x][i] == 0) { continue; }
          g[y].push_back(Edge(y, x, poly[y][x][i]));
        }
      }
      Matrix flow;
      ans[i] = MaxFlow(g, 0, n - 1, flow);
      if (i != 0) {
        REP(y, n) {
          REP(x, n) {
            if (poly[y][x][i] - flow[y][x] == 0) { continue; }
            if (poly[y][x][i] + flow[y][x] == 0) { continue; }
            poly[y][x][i - 1] = INF;
          }
        }
      }
    }
    PrintAns(ans);
  }
}

Measured memory_bytes: 2580