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;
struct Edge {
  int x, y, w, id;
  bool operator<(const Edge &A) const { return w < A.w; }
} edge[100005];
struct DisJointSet {
  int rank[100005], parent[100005];
  void init(int n) {
    for (int i = 0; i < n; i++) {
      rank[i] = 0;
      parent[i] = i;
    }
  }
  int Find(int x) {
    if (parent[x] == x) return x;
    return parent[x] = Find(parent[x]);
  }
  void Union(int x, int y) {
    x = Find(x);
    y = Find(y);
    if (x == y) return;
    if (rank[x] >= rank[y]) {
      parent[y] = x;
      if (rank[x] == rank[y]) rank[x]++;
    } else {
      parent[x] = y;
    }
  }
} ufset;
int V;
bool visit[100005];
vector<pair<int, int> > graph[100005];
map<int, int> mp;
int dfn[100005], low[100005], tag[100005];
bool cmp_id(const Edge &A, const Edge &B) { return A.id < B.id; }
void Tarjan(int fa, int u, int dep) {
  dfn[u] = low[u] = dep;
  for (int i = 0; i < graph[u].size(); i++) {
    int v = graph[u][i].first;
    int id = graph[u][i].second;
    if (dfn[v] == -1) {
      visit[id] = true;
      Tarjan(u, v, dep + 1);
      low[u] = min(low[u], low[v]);
      if (low[v] > dfn[u]) tag[id] = 1;
    } else if (!visit[id]) {
      low[u] = min(low[u], dfn[v]);
    }
  }
}
void Bridge() {
  for (int i = 0; i < V; i++) dfn[i] = -1;
  for (int i = 0; i < V; i++)
    if (dfn[i] == -1) Tarjan(-1, i, 0);
}
int main() {
  memset(tag, -1, sizeof(tag));
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    cin >> edge[i].x >> edge[i].y >> edge[i].w;
    edge[i].id = i;
  }
  sort(edge, edge + m);
  int l = 0, r;
  ufset.init(n);
  while (l < m) {
    r = l;
    while (r < m && edge[r].w == edge[l].w) {
      r++;
    }
    mp.clear();
    for (int i = l; i < r; i++) {
      int fx = ufset.Find(edge[i].x), fy = ufset.Find(edge[i].y);
      if (fx == fy) {
        tag[edge[i].id] = 0;
      } else {
        mp[fx] = mp[fy] = 0;
      }
    }
    V = 0;
    for (map<int, int>::iterator it = mp.begin(); it != mp.end(); it++) {
      it->second = V;
      V++;
    }
    for (int i = 0; i < V; i++) graph[i].clear();
    for (int i = l; i < r; i++) {
      int fx = ufset.Find(edge[i].x), fy = ufset.Find(edge[i].y);
      if (fx == fy) continue;
      int a = mp[fx], b = mp[fy];
      graph[a].push_back(make_pair(b, edge[i].id));
      graph[b].push_back(make_pair(a, edge[i].id));
    }
    Bridge();
    for (int i = l; i < r; i++) ufset.Union(edge[i].x, edge[i].y);
    l = r;
  }
  sort(edge, edge + m, cmp_id);
  for (int i = 0; i < m; i++) {
    if (tag[i] == 1) {
      cout << "any" << endl;
    } else if (tag[i] == 0) {
      cout << "none" << endl;
    } else {
      cout << "at least one" << endl;
    }
  }
  return 0;
}
