You have unweighted tree of $n$ vertices. You have to assign a positive weight to each edge so that the following condition would hold:

  For every two different leaves $v_{1}$ and $v_{2}$ of this tree, bitwise XOR of weights of all edges on the simple path between $v_{1}$ and $v_{2}$ has to be equal to $0$. 

Note that you can put very large positive integers (like $10^{(10^{10})}$).

It's guaranteed that such assignment always exists under given constraints. Now let's define $f$ as the number of distinct weights in assignment.

 [Image] In this example, assignment is valid, because bitwise XOR of all edge weights between every pair of leaves is $0$. $f$ value is $2$ here, because there are $2$ distinct edge weights($4$ and $5$).

[Image] In this example, assignment is invalid, because bitwise XOR of all edge weights between vertex $1$ and vertex $6$ ($3, 4, 5, 4$) is not $0$. 

What are the minimum and the maximum possible values of $f$ for the given tree? Find and print both.


-----Input-----

The first line contains integer $n$ ($3 \le n \le 10^{5}$) — the number of vertices in given tree.

The $i$-th of the next $n-1$ lines contains two integers $a_{i}$ and $b_{i}$ ($1 \le a_{i} \lt b_{i} \le n$) — it means there is an edge between $a_{i}$ and $b_{i}$. It is guaranteed that given graph forms tree of $n$ vertices.


-----Output-----

Print two integers — the minimum and maximum possible value of $f$ can be made from valid assignment of given tree. Note that it's always possible to make an assignment under given constraints.


-----Examples-----
Input
6
1 3
2 3
3 4
4 5
5 6

Output
1 4

Input
6
1 3
2 3
3 4
4 5
4 6

Output
3 3

Input
7
1 2
2 7
3 4
4 7
5 6
6 7

Output
1 6



-----Note-----

In the first example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum.  [Image] 

In the second example, possible assignments for each minimum and maximum are described in picture below. The $f$ value of valid assignment of this tree is always $3$.  [Image] 

In the third example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum.  [Image]

```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\nfrom collections import deque\ninput = sys.stdin.readline\n\nn = int(input())\ninfo = [list(map(int, input().split())) for i in range(n - 1)]\n\ntree = [[] for i in range(n)]\nfor a, b in info:\n    a -= 1\n    b -= 1\n    tree[a].append(b)\n    tree[b].append(a)\n    \nmax_ = n - 1\nfor v in range(n):\n    cnt = 0\n    for nxt_v in tree[v]:\n        if len(tree[nxt_v]) == 1:\n            cnt += 1\n    max_ -= max(cnt - 1, 0)\n    \n    \nvisited = [-1] * n\nq = deque([0])\nvisited[0] = 0\nwhile q:\n    v = q.popleft()\n    for nxt_v in tree[v]:\n        if visited[nxt_v] != -1:\n            continue\n        visited[nxt_v] = visited[v] + 1\n        q.append(nxt_v)\n\n\nmin_ = 3\nfor i in range(n):\n    if len(tree[i]) == 1:\n        if visited[i] % 2 == 0:\n            break\nelse:\n    min_ = 1\n\nfor i in range(n):\n    if len(tree[i]) == 1:\n        if (visited[i] + 1) % 2 == 0:\n            break\nelse:\n    min_ = 1\nprint(min_, max_)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14259