Given is an undirected connected graph with N vertices numbered 1 to N, and M edges numbered 1 to M.
The given graph may contain multi-edges but not self loops.
Each edge has an integer label between 1 and N (inclusive).
Edge i has a label c_i, and it connects Vertex u_i and v_i bidirectionally.
Snuke will write an integer between 1 and N (inclusive) on each vertex (multiple vertices may have the same integer written on them) and then keep only the edges satisfying the condition below, removing the other edges.
Condition: Let x and y be the integers written on the vertices that are the endpoints of the edge. Exactly one of x and y equals the label of the edge.
We call a way of writing integers on the vertices good if (and only if) the graph is still connected after removing the edges not satisfying the condition above. Determine whether a good way of writing integers exists, and present one such way if it exists.

-----Constraints-----
 - 2 \leq N \leq 10^5
 - N-1 \leq M \leq 2 \times 10^5
 - 1 \leq u_i,v_i,c_i \leq N
 - The given graph is connected and has no self-loops.

-----Input-----
Input is given from Standard Input in the following format:
N M
u_1 v_1 c_1
\vdots
u_M v_M c_M

-----Output-----
If there is no good way of writing integers, print No.
Otherwise, print N lines. The i-th line should contain the integer written on Vertex i.
Any good way of writing integers will be accepted.

-----Sample Input-----
3 4
1 2 1
2 3 2
3 1 3
1 3 1

-----Sample Output-----
1
2
1

 - We write 1, 2, and 1 on Vertex 1, 2, and 3, respectively.
 - Edge 1 connects Vertex 1 and 2, and its label is 1.
 - Only the integer written on Vertex 1 equals the label, so this edge will not get removed.
 - Edge 2 connects Vertex 2 and 3, and its label is 2.
 - Only the integer written on Vertex 2 equals the label, so this edge will not be removed.
 - Edge 3 connects Vertex 1 and 3, and its label is 3.
 - Both integers written on the vertices differ from the label, so this edge will be removed.
 - Edge 4 connects Vertex 1 and 3, and its label is 1.
 - Both integers written on the vertices equal the label, so this edge will be removed.
 - After Edge 3 and 4 are removed, the graph will still be connected, so this is a good way of writing integers.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ninput = sys.stdin.readline\nfrom collections import defaultdict, deque\nmod = 10 ** 9 + 7; INF = float("inf")\n\ndef getlist():\n\treturn list(map(int, input().split()))\n\nclass UnionFind(object):\n\tdef __init__(self, N):\n\t\tself.par = [i for i in range(N)]\n\t\tself.rank = [0] * N\n\n\tdef find(self, x):\n\t\tif self.par[x] == x:\n\t\t\treturn x\n\t\telse:\n\t\t\tself.par[x] = self.find(self.par[x])\n\t\t\treturn self.par[x]\n\n\tdef same_check(self, x, y):\n\t\treturn self.find(x) == self.find(y)\n\n\tdef union(self, x, y):\n\t\tx = self.find(x); y = self.find(y)\n\t\tif self.rank[x] < self.rank[y]:\n\t\t\tself.par[x] = y\n\t\telse:\n\t\t\tself.par[y] = x\n\t\t\tif self.rank[x] == self.rank[y]:\n\t\t\t\tself.rank[x] += 1\n\nclass Graph(object):\n\tdef __init__(self, N):\n\t\tself.graph = [[] for i in range(N)]\n\n\tdef add_edge(self, a, b, c):\n\t\tself.graph[a].append((b, c))\n\ndef bfs(G, s, N):\n\tQ = deque(); Q.append(s)\n\tvisit = [0] * N; visit[s] = 1\n\tlabel = [None] * N; label[s] = 0\n\twhile Q:\n\t\tv = Q.popleft()\n\t\tfor i, c in G.graph[v]:\n\t\t\tif visit[i] == 0:\n\t\t\t\tvisit[i] = 1\n\t\t\t\tif c != label[v]:\n\t\t\t\t\tlabel[i] = c\n\t\t\t\telse:\n\t\t\t\t\tif c == N - 1:\n\t\t\t\t\t\tlabel[i] = 0\n\t\t\t\t\telse:\n\t\t\t\t\t\tlabel[i] = N - 1\n\t\t\t\tQ.append(i)\n\treturn label\n\ndef main():\n\tN, M = getlist()\n\tG = Graph(N)\n\tUF = UnionFind(N)\n\tfor i in range(M):\n\t\tu, v, c = getlist()\n\t\tu -= 1; v -= 1; c -= 1\n\t\tif UF.same_check(u, v) == False:\n\t\t\tUF.union(u, v)\n\t\t\tG.add_edge(u, v, c)\n\t\t\tG.add_edge(v, u, c)\n\n\tans = bfs(G, 0, N)\n\tfor i in ans:\n\t\tprint(i + 1)\n\n\ndef __starting_point():\n\tmain()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 21297