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 = 1e5 + 17;
vector<pair<int, int>> ve, vec[N];
bool f[N];
int dis[N], h[N], par[N], a[N], b[N], wi[N], ans[N], pos[N];
int root(int x) {
  while (par[x] != 0) {
    x = par[x];
  }
  return x;
}
void merge(int x, int y) {
  x = root(x);
  y = root(y);
  vec[x].clear();
  vec[y].clear();
  f[x] = false;
  f[y] = false;
  if (x == y) {
    return;
  }
  if (h[x] > h[y]) {
    par[y] = x;
  } else {
    par[x] = y;
    if (h[x] == h[y]) {
      h[y]++;
    }
  }
}
void add(int x, int y, int z) {
  if (x == y) {
    return;
  }
  ans[z] = 1;
  vec[x].push_back({y, z});
  vec[y].push_back({x, z});
}
void dfs(int x, int y, int hi) {
  f[x] = true;
  dis[x] = hi;
  for (auto u : vec[x]) {
    if (!f[u.first]) {
      dfs(u.first, u.second, hi + 1);
      dis[x] = min(dis[x], dis[u.first]);
    } else if (u.second != y) {
      dis[x] = min(dis[x], dis[u.first]);
    }
  }
  if (dis[x] == hi) {
    ans[y] = 2;
  }
}
bool migam(int &aa, int &bb) { return wi[aa] < wi[bb]; }
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    cin >> a[i] >> b[i] >> wi[i];
    pos[i] = i;
  }
  sort(pos + 1, pos + m + 1, migam);
  for (int i = 1; i <= m;) {
    int j;
    if (i == 1) {
    }
    for (j = i; wi[pos[j]] == wi[pos[i]]; j++) {
      add(root(a[pos[j]]), root(b[pos[j]]), pos[j]);
    }
    for (j = i; wi[pos[j]] == wi[pos[i]]; j++) {
      int k = root(a[pos[j]]);
      if (!f[k]) {
        dfs(k, 0, 0);
      }
    }
    for (j = i; wi[pos[i]] == wi[pos[j]]; j++) {
      merge(a[pos[j]], b[pos[j]]);
    }
    i = j;
  }
  for (int i = 1; i <= m; i++) {
    if (!ans[i]) {
      cout << "none" << endl;
    } else if (ans[i] == 1) {
      cout << "at least one" << endl;
    } else {
      cout << "any" << endl;
    }
  }
  return 0;
}
