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 mod = 1e9 + 7;
const int inf = 1e9;
int add(int x, int y) { return (1ll * x + 1ll * y) % mod; }
int del(int x, int y) { return ((1ll * x - 1ll * y) % mod + mod) % mod; }
int mul(int x, int y) { return (1ll * x * 1ll * y) % mod; }
const int N = 1e5 + 5;
int pSet[N], n, m, res[N], low[N], num[N], cnt, vis[N], par[N];
vector<pair<pair<int, int>, pair<int, int>>> edge;
int findSet(int u) {
  if (u == pSet[u])
    return u;
  else
    return pSet[u] = findSet(pSet[u]);
}
bool sameSet(int u, int v) { return (findSet(u) == findSet(v)); }
void unionSet(int u, int v) { pSet[findSet(u)] = findSet(v); }
vector<pair<int, int>> graph[N];
map<pair<int, int>, int> Edge;
void dfs(int u) {
  vis[u] = 1;
  low[u] = num[u] = ++cnt;
  for (int i = 0; i < graph[u].size(); i++) {
    int v = graph[u][i].first, id = graph[u][i].second;
    if (!vis[v]) {
      par[v] = u;
      dfs(v);
      low[u] = min(low[u], low[v]);
      if (num[u] < low[v] && Edge[{u, v}] == 1) res[id] = 2;
    } else if (par[u] != v)
      low[u] = min(low[u], num[v]);
  }
}
int main() {
  cin.tie(0), ios::sync_with_stdio(0);
  cin >> n >> m;
  for (int i = 1; i <= n; i++) pSet[i] = i;
  for (int i = 1; i <= m; i++) {
    int u, v, c;
    cin >> u >> v >> c;
    edge.push_back({{c, i}, {u, v}});
  }
  sort(edge.begin(), edge.end());
  for (int i = 0; i < edge.size(); i++) {
    int j = i;
    while (j < edge.size() && edge[j].first.first == edge[i].first.first) j++;
    j--;
    for (int k = i; k <= j; k++) {
      int id = edge[k].first.second, u = edge[k].second.first,
          v = edge[k].second.second;
      if (sameSet(u, v) == 0) res[id] = 1;
    }
    for (int k = i; k <= j; k++) {
      int id = edge[k].first.second, u = edge[k].second.first,
          v = edge[k].second.second;
      if (sameSet(u, v) == 0) {
        Edge[{findSet(u), findSet(v)}]++;
        Edge[{findSet(v), findSet(u)}]++;
        graph[findSet(u)].push_back({findSet(v), id});
        graph[findSet(v)].push_back({findSet(u), id});
      }
    }
    cnt = 0;
    for (int k = i; k <= j; k++) {
      int u = edge[k].second.first, v = edge[k].second.second;
      if (sameSet(u, v) == 0) {
        if (!vis[findSet(u)]) dfs(findSet(u));
        if (!vis[findSet(v)]) dfs(findSet(v));
      }
    }
    for (int k = i; k <= j; k++) {
      int u = edge[k].second.first, v = edge[k].second.second;
      if (sameSet(u, v) == 0) {
        graph[findSet(u)].clear();
        graph[findSet(v)].clear();
        vis[findSet(u)] = low[findSet(u)] = num[findSet(u)] = 0;
        vis[findSet(v)] = low[findSet(v)] = num[findSet(v)] = 0;
        Edge[{findSet(u), findSet(v)}] = Edge[{findSet(v), findSet(u)}] = 0;
      }
    }
    for (int k = i; k <= j; k++) {
      int u = edge[k].second.first, v = edge[k].second.second;
      if (sameSet(u, v) == 0) unionSet(u, v);
    }
    i = j;
  }
  for (int i = 1; i <= m; i++) {
    if (res[i] == 0)
      cout << "none\n";
    else if (res[i] == 1)
      cout << "at least one\n";
    else
      cout << "any\n";
  }
}
