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 MAX = 1e5 + 9;
const int MAX2 = 1e6 + 9;
vector<pair<int, int> > g[MAX];
vector<pair<pair<int, int>, int> > edge[MAX2];
int n, m, u, v, w, f[MAX], h[MAX];
string ans[MAX];
bool mark[MAX];
vector<int> ve;
int root(int v) { return f[v] < 0 ? v : f[v] = root(f[v]); }
void merge(int v, int u) {
  v = root(v);
  u = root(u);
  if (v == u) return;
  if (f[u] < f[v]) swap(v, u);
  f[v] += f[u], f[u] = v;
}
int dfs(int v, int p = -1) {
  mark[v] = true;
  int ret = 1e9;
  for (auto u : g[v])
    if (u.second != p) {
      if (mark[u.first] == false) {
        h[u.first] = h[v] + 1;
        int r = dfs(u.first, u.second);
        ret = min(ret, r);
        if (r <= h[v]) ans[u.second] = "at least one";
      } else {
        ret = min(ret, h[u.first]);
        ans[u.second] = "at least one";
      }
    }
  return ret;
}
int32_t main() {
  memset(f, -1, sizeof f);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    cin >> v >> u >> w;
    v--, u--;
    edge[w].push_back({{v, u}, i});
  }
  for (int i = 0; i < MAX2; i++) {
    for (auto e : edge[i]) {
      int a = root(e.first.first), b = root(e.first.second);
      if (a == b) {
        ans[e.second] = "none";
        continue;
      }
      g[a].push_back({b, e.second});
      g[b].push_back({a, e.second});
      ve.push_back(a);
      ve.push_back(b);
    }
    for (auto i : ve)
      if (mark[i] == false) {
        h[i] = 0;
        dfs(i);
      }
    for (auto e : edge[i]) merge(e.first.first, e.first.second);
    for (auto i : ve) {
      mark[i] = false;
      g[i].clear();
    }
    ve.clear();
  }
  for (int i = 0; i < m; i++) cout << (ans[i] == "" ? "any" : ans[i]) << endl;
}
