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 Counter,deque\n\nn,m=map(int,input().split())\nE=[list(map(int,input().split())) for i in range(m)]\n\nF=[]\n\n# E = [(cost, v, w), ...]\n#   G上の全ての辺(v, w)とそのcostを含むlist\n\n# Union-Findを使うことで頂点間の連結判定を行う\n\n*p, = range(n)\ndef root(x):\n    if x == p[x]:\n        return x\n    p[x] = y = root(p[x])\n    return y\n\ndef unite(x, y):\n    px = root(x); py = root(y)\n    if px == py:\n        return 0\n    if px < py:\n        p[py] = px\n    else:\n        p[px] = py\n    return 1\n\nE.sort()\nans = 0\nfor  v, w, c in E:\n    if unite(v-1, w-1):\n        F.append([v,w,c])\n        ans += c\n\n# ansが最小全域木の解\n\ng=[[] for i in range(n)]\nans=[0]*n\nans[0]='?'\nused=[False]*(n+1)\npre=[0]*n\n \nfor u,v,c in F:\n    g[u-1].append([v-1,c])\n    g[v-1].append([u-1,c])\n\n \n \nQ=deque()\nQ.append((0))\n \nwhile Q:\n    p=Q.popleft()\n \n    for s in g[p]:\n        i,v=s[0],s[1]\n        if ans[i]==0:\n            if ans[p]==v:\n                ans[i]=v+1\n                Q.append((i))\n                if ans[i]==n+1:\n                    ans[i]=1\n            else:\n                ans[i]=v\n                Q.append((i))\n \n \nfor i,v in g[0]:\n    used[v]=True\n \nfor i in range(1,n+1):\n    if used[i]==False:\n        ans[0]=i\n        break\n \n \nprint(*ans,sep='\\n')"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14443