One of Chef's friends offered him a deal: during $D$ days, they are going to exchange money. For each $i$ ($1 \le i \le D$), on the $i$-th day, Chef's friend would give Chef $A$ rupees, while Chef would give his friend $2^{i-1}$ rupees ($1$ rupee on day $1$, $2$ rupees on day $2$, $4$ rupees on day $3$, and so on). Chef's profit from the deal is the total number of rupees he received from his friend minus the total number of rupees he gave his friend.
Chef decided to ask for your advice before accepting the deal. You want to help him by telling him two numbers $D_1$ and $D_2$, where $D_1$ is the maximum value of $D$ such that Chef should accept the deal, i.e. his profit from the deal is positive if $D = D_1$, and $D_2$ is the value of $D$ that leads to the maximum possible profit for Chef. If there are multiple values of $D$ that lead to the maximum profit, $D_2$ is the smallest of these values.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single integer $A$.

-----Output-----
For each test case, print a single line containing two space-separated integers $D_1$ and $D_2$.

-----Constraints-----
- $1 \le T \le 100,000$
- $5 \le A \le 10^9$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
4
5
8
9
1000000000

-----Example Output-----
4 3
5 3
5 4
35 30

```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 = '# cook your dish here - pyt3\ndef fun(a):\n t1 = 1\n t2 = a\n p = a - 1\n pday=1\n count = 1\n while t2>t1:\n  t2 += a\n  t1 = 1 + (2*t1)\n  if t2-t1>p:\n   p = max(p, t2-t1)\n   pday = count\n  count += 1\n return count-1, pday+1\n\ntry:\n t = int(input())\n for i in range(t):\n  n = int(input())\n  x = fun(n)\n  print(x[0], x[1])\nexcept Exception:\n pass'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13081