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;
int n, m;
tuple<int, int, int> edges[100000];
int type_of_edge[100000];
vector<int> tarjan_edges[100000];
int disc[100000];
int lowest[100000];
inline int get_dad(int me, vector<int>& dads) {
  int tmp;
  while (me != dads[me]) tmp = dads[me], dads[me] = dads[dads[me]], me = tmp;
  return me;
}
void dfs(int me, int come_by_edge_id, int& t, vector<int>& dad) {
  int me_dad = dad[me];
  disc[me_dad] = t++;
  lowest[me_dad] = disc[me_dad];
  for (int e_id : tarjan_edges[me_dad])
    if (e_id != come_by_edge_id) {
      int other = (get_dad(get<0>(edges[e_id]), dad) == get_dad(me, dad))
                      ? get<1>(edges[e_id])
                      : get<0>(edges[e_id]);
      int other_dad = get_dad(other, dad);
      if (disc[other_dad] != -1)
        lowest[me_dad] = min(lowest[me_dad], lowest[other_dad]),
        lowest[me_dad] = min(lowest[me_dad], disc[other_dad]);
    }
  for (int e_id : tarjan_edges[me_dad])
    if (e_id != come_by_edge_id) {
      int other = (get_dad(get<0>(edges[e_id]), dad) == get_dad(me, dad))
                      ? get<1>(edges[e_id])
                      : get<0>(edges[e_id]);
      int other_dad = get_dad(other, dad);
      if (disc[other_dad] == -1) dfs(other, e_id, t, dad);
    }
  for (int e_id : tarjan_edges[me_dad])
    if (e_id != come_by_edge_id) {
      int other = (get_dad(get<0>(edges[e_id]), dad) == get_dad(me, dad))
                      ? get<1>(edges[e_id])
                      : get<0>(edges[e_id]);
      int other_dad = get_dad(other, dad);
      lowest[me_dad] = min(lowest[me_dad], lowest[other_dad]);
      lowest[me_dad] = min(lowest[me_dad], disc[other_dad]);
    }
}
void mark_edges(const vector<int>& edge_idxs, vector<int>& dad) {
  for (int e_id : edge_idxs) {
    int a_dad = get_dad(get<0>(edges[e_id]), dad);
    int b_dad = get_dad(get<1>(edges[e_id]), dad);
    tarjan_edges[a_dad].clear();
    tarjan_edges[b_dad].clear();
    disc[a_dad] = -1;
    disc[b_dad] = -1;
  }
  for (int e_id : edge_idxs) {
    int a_dad = get_dad(get<0>(edges[e_id]), dad);
    int b_dad = get_dad(get<1>(edges[e_id]), dad);
    tarjan_edges[a_dad].push_back(e_id);
    tarjan_edges[b_dad].push_back(e_id);
  }
  for (int e_id : edge_idxs) {
    int a = get<0>(edges[e_id]);
    int a_dad = get_dad(a, dad);
    int t = 0;
    if (disc[a_dad] == -1) dfs(a, -1, t, dad);
  }
  for (int e_id : edge_idxs) {
    int a = get<0>(edges[e_id]);
    int b = get<1>(edges[e_id]);
    int a_dad = get_dad(a, dad);
    int b_dad = get_dad(b, dad);
    if (disc[a_dad] > disc[b_dad]) swap(a_dad, b_dad);
    if (disc[a_dad] < lowest[b_dad])
      type_of_edge[e_id] = 2;
    else
      type_of_edge[e_id] = 1;
  }
}
void compute_mst_like() {
  vector<int> sorted_edges(m, -1);
  vector<int> dad(n, -1);
  vector<int> sizes(n, 1);
  for (int i = 0; i < m; ++i) sorted_edges[i] = i;
  sort(sorted_edges.begin(), sorted_edges.end(),
       [](const int& l, const int& r) {
         return get<2>(edges[l]) < get<2>(edges[r]);
       });
  for (int i = 0; i < n; ++i) dad[i] = i;
  int max_size = 1;
  int sorted_edges_idx = -1;
  while (max_size != n) {
    vector<int> edges_to_join;
    do {
      sorted_edges_idx++;
      int a = get<0>(edges[sorted_edges[sorted_edges_idx]]);
      int b = get<1>(edges[sorted_edges[sorted_edges_idx]]);
      int a_dad = get_dad(a, dad);
      int b_dad = get_dad(b, dad);
      if (a_dad != b_dad)
        edges_to_join.push_back(sorted_edges[sorted_edges_idx]);
    } while (sorted_edges_idx < m - 1 &&
             get<2>(edges[sorted_edges[sorted_edges_idx]]) ==
                 get<2>(edges[sorted_edges[sorted_edges_idx + 1]]));
    mark_edges(edges_to_join, dad);
    for (int e_id : edges_to_join) {
      int a_dad = get_dad(get<0>(edges[e_id]), dad);
      int b_dad = get_dad(get<1>(edges[e_id]), dad);
      if (a_dad != b_dad) {
        if (sizes[a_dad] < sizes[b_dad])
          dad[a_dad] = b_dad, sizes[b_dad] += sizes[a_dad],
          max_size = max(max_size, sizes[b_dad]);
        else
          dad[b_dad] = a_dad, sizes[a_dad] += sizes[b_dad],
          max_size = max(max_size, sizes[a_dad]);
      }
    }
  }
}
int main() {
  std::ios_base::sync_with_stdio(false);
  cin >> n >> m;
  for (int i = 0; i < m; ++i)
    cin >> get<0>(edges[i]) >> get<1>(edges[i]) >> get<2>(edges[i]),
        get<0>(edges[i]) -= 1, get<1>(edges[i]) -= 1;
  for (int i = 0; i < m; ++i) type_of_edge[i] = 0;
  compute_mst_like();
  for (int i = 0; i < m; ++i)
    if (type_of_edge[i] == 0)
      cout << "none\n";
    else if (type_of_edge[i] == 1)
      cout << "at least one\n";
    else
      cout << "any\n";
  return 0;
}
