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 long long int maxn = 1e5 + 5, M = 1e6 + 6, inf = 1e9;
const long long int bghs = 1e9 + 7;
vector<pair<long long int, long long int> > g[maxn];
vector<pair<pair<long long int, long long int>, long long int> > edge[M];
long long int n, m, par[maxn], h[maxn];
long long int ans[maxn];
bool mark[maxn];
vector<long long int> nmd;
long long int gpc(long long int v) {
  return par[v] < 0 ? v : par[v] = gpc(par[v]);
}
void mrg(long long int v, long long int u) {
  u = gpc(u);
  v = gpc(v);
  if (v == u) return;
  if (par[u] < par[v]) swap(v, u);
  par[v] += par[u];
  par[u] = v;
}
long long int dfs(long long int v, long long int p = -1) {
  mark[v] = true;
  long long int res = inf;
  for (auto u : g[v])
    if (u.second != p) {
      if (!mark[u.first]) {
        h[u.first] = h[v] + 1;
        long long int r = dfs(u.first, u.second);
        res = min(res, r);
        if (r <= h[v]) ans[u.second] = 1;
      } else {
        res = min(res, h[u.first]);
        ans[u.second] = 1;
      }
    }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  memset(par, -1, sizeof par);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    long long int u, v, w;
    cin >> v >> u >> w;
    v--;
    u--;
    edge[w].push_back({{v, u}, i});
  }
  for (int i = 0; i < M; i++) {
    for (auto e : edge[i]) {
      long long int u = gpc(e.first.first);
      long long int v = gpc(e.first.second);
      if (u == v) {
        ans[e.second] = 2;
        continue;
      }
      g[u].push_back({v, e.second});
      g[v].push_back({u, e.second});
      nmd.push_back(u);
      nmd.push_back(v);
    }
    for (auto i : nmd)
      if (!mark[i]) {
        h[i] = 0;
        dfs(i);
      }
    for (auto e : edge[i]) mrg(e.first.first, e.first.second);
    for (auto i : nmd) {
      mark[i] = false;
      g[i].clear();
    }
    nmd.clear();
  }
  for (int i = 0; i < m; i++) {
    if (ans[i] == 0)
      cout << "any\n";
    else if (ans[i] == 1)
      cout << "at least one\n";
    else
      cout << "none\n";
  }
}
