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 MAXN = 1001 * 1001;
struct yal {
  int u, v, ind;
};
vector<yal> a[MAXN];
vector<pair<int, int> > v;
int ans[MAXN] = {}, par[MAXN] = {}, sz[MAXN] = {};
int mark[MAXN] = {}, mark2[MAXN] = {}, t[MAXN] = {}, dp[MAXN] = {};
vector<pair<int, int> > adj[MAXN] = {};
inline yal make_yal(int u, int v, int ind) {
  yal ans;
  ans.u = u;
  ans.v = v;
  ans.ind = ind;
  return ans;
}
int get_par(int u) { return (par[u] == u ? u : par[u] = get_par(par[u])); }
inline void merge(int a, int b) {
  int x = get_par(a), y = get_par(b);
  if (x == y) return;
  if (sz[x] > sz[y]) swap(x, y);
  sz[y] += sz[x];
  par[x] = y;
}
vector<int> q;
void dfs(int u, int p) {
  mark2[u] = 1;
  dp[u] = t[u];
  for (auto v : adj[u]) {
    if (v.second == p) continue;
    if (mark2[v.first]) {
      dp[u] = min(t[v.first], dp[u]);
      continue;
    }
    t[v.first] = t[u] + 1;
    dfs(v.first, v.second);
    if (dp[v.first] > t[u]) ans[v.second] = 1;
    dp[u] = min(dp[v.first], dp[u]);
  }
}
int main() {
  int n, m, x, y, z;
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; i++) {
    scanf("%d%d%d", &x, &y, &z);
    a[z].push_back(make_yal(x, y, i));
  }
  for (int i = 1; i <= n; i++) {
    sz[i] = 1;
    par[i] = i;
    mark2[i] = 1;
  }
  for (int i = 0; i < MAXN; i++) {
    n = a[i].size();
    if (!n) continue;
    q.clear();
    v.clear();
    for (int j = 0; j < n; j++) {
      x = get_par(a[i][j].u), y = get_par(a[i][j].v);
      if (x != y) {
        if (mark2[x]) q.push_back(x);
        if (mark2[y]) q.push_back(y);
        mark2[x] = 0;
        mark2[y] = 0;
        ans[a[i][j].ind] = 2;
        adj[y].push_back({x, a[i][j].ind});
        adj[x].push_back({y, a[i][j].ind});
        v.push_back({x, y});
      }
    }
    for (auto u : q)
      if (!mark2[u]) {
        t[u] = 0;
        dfs(u, -1);
      }
    for (auto u : q) adj[u].clear();
    for (auto u : v) merge(u.first, u.second);
  }
  for (int i = 0; i < m; i++) {
    if (ans[i] == 0) puts("none");
    if (ans[i] == 1) puts("any");
    if (ans[i] == 2) puts("at least one");
  }
}
