You are given a connected weighted undirected graph without any loops and multiple edges. 

Let us remind you that a graph's spanning tree is defined as an acyclic connected subgraph of the given graph that includes all of the graph's vertexes. The weight of a tree is defined as the sum of weights of the edges that the given tree contains. The minimum spanning tree (MST) of a graph is defined as the graph's spanning tree having the minimum possible weight. For any connected graph obviously exists the minimum spanning tree, but in the general case, a graph's minimum spanning tree is not unique.

Your task is to determine the following for each edge of the given graph: whether it is either included in any MST, or included at least in one MST, or not included in any MST.

Input

The first line contains two integers n and m (2 ≤ n ≤ 105, <image>) — the number of the graph's vertexes and edges, correspondingly. Then follow m lines, each of them contains three integers — the description of the graph's edges as "ai bi wi" (1 ≤ ai, bi ≤ n, 1 ≤ wi ≤ 106, ai ≠ bi), where ai and bi are the numbers of vertexes connected by the i-th edge, wi is the edge's weight. It is guaranteed that the graph is connected and doesn't contain loops or multiple edges.

Output

Print m lines — the answers for all edges. If the i-th edge is included in any MST, print "any"; if the i-th edge is included at least in one MST, print "at least one"; if the i-th edge isn't included in any MST, print "none". Print the answers for the edges in the order in which the edges are specified in the input.

Examples

Input

4 5
1 2 101
1 3 100
2 3 2
2 4 2
3 4 1


Output

none
any
at least one
at least one
any


Input

3 3
1 2 1
2 3 1
1 3 2


Output

any
any
none


Input

3 3
1 2 1
2 3 1
1 3 1


Output

at least one
at least one
at least one

Note

In the second sample the MST is unique for the given graph: it contains two first edges.

In the third sample any two edges form the MST for the given graph. That means that each edge is included at least in one MST.
#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 5;
const int mod = 1e9 + 7;
int s, i, j, n, m, x, y, z;
int low[N], first[N], pred[N], ans[N], ata[N];
vector<pair<int, pair<int, int> > > v[N];
vector<pair<int, int> > V[N];
vector<int> q;
int atabul(int x) { return ata[x] == x ? x : ata[x] = atabul(ata[x]); }
void fb(int x) {
  int i, cnt = 0;
  low[x] = first[x] = ++s;
  for (i = 0; i < V[x].size(); i++) {
    if (!first[V[x][i].first]) {
      pred[V[x][i].first] = x;
      fb(V[x][i].first);
      low[x] = min(low[x], low[V[x][i].first]);
      if (low[V[x][i].first] > first[x]) ans[V[x][i].second] = 2;
    } else if (V[x][i].first != pred[x])
      low[x] = min(low[x], first[V[x][i].first]);
    else
      cnt++;
  }
  if (cnt >= 2) low[x] = min(low[x], first[pred[x]]);
  return;
}
int main() {
  scanf("%d %d", &n, &m);
  for (i = 1; i <= m; i++) {
    scanf("%d %d %d", &x, &y, &z);
    v[z].push_back(make_pair(i, make_pair(x, y)));
  }
  for (i = 1; i <= n; i++) ata[i] = i;
  for (i = 1; i <= N - 5; i++) {
    q.clear();
    for (j = 0; j < v[i].size(); j++)
      if (atabul(v[i][j].second.first) != atabul(v[i][j].second.second)) {
        V[atabul(v[i][j].second.first)].push_back(
            make_pair(atabul(v[i][j].second.second), v[i][j].first));
        V[atabul(v[i][j].second.second)].push_back(
            make_pair(atabul(v[i][j].second.first), v[i][j].first));
        q.push_back(atabul(v[i][j].second.first));
        q.push_back(atabul(v[i][j].second.second));
        ans[v[i][j].first] = 1;
      }
    for (j = 0; j < q.size(); j++) first[q[j]] = 0;
    for (j = 0; j < q.size(); j++)
      if (!first[q[j]]) fb(q[j]);
    for (j = 0; j < q.size(); j++) V[q[j]].clear();
    for (j = 0; j < v[i].size(); j++)
      if (atabul(v[i][j].second.first) != atabul(v[i][j].second.second))
        ata[atabul(v[i][j].second.first)] = atabul(v[i][j].second.second);
  }
  for (i = 1; i <= m; i++)
    if (ans[i] == 2)
      puts("any");
    else if (ans[i])
      puts("at least one");
    else
      puts("none");
}
