Arya and Aryan live in a country called Nadaca. Nadaca consists of $N$ cities numbered $1$ through $N$, which are connected by some bidirectional roads. Each road has a positive (not necessarily integer) length. Arya lives in city $1$ and Aryan lives in city $N$.
Arya claims that for each city $v$, the shortest path from city $1$ to city $v$ has length $a_v$. Aryan does not disagree, but claims that for each city $v$, the shortest path from city $N$ to city $v$ has length $b_v$. You are the wisest person they know, so they asked you to tell them if it is possible for their claims to be true, i.e. if a road network which fully satisfies their claims exists. Help them!

-----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 line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $a_1, a_2, \ldots, a_N$.
- The third line contains $N$ space-separated integers $b_1, b_2, \ldots, b_N$.

-----Output-----
For each test case, print a single line containing the string "Yes" if Arya's and Aryan's claims can be true or "No" otherwise.

-----Constraints-----
- $1 \le T \le 10^3$
- $2 \le N \le 10^6$
- $0 \le a_i, b_i \le 10^9$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (50 points): the sum of $N$ over all test cases does not exceed $10^3$
Subtask #2 (50 points): original constraints

-----Example Input-----
2
3
0 1 1
1 1 0
3
0 1 5
5 1 0

-----Example Output-----
Yes
No

```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 = 'for _ in range(int(input())):\n n=int(input())\n A=list(map(int,input().split(" ")))\n B=list(map(int,input().split(" ")))\n ans="Yes"\n\n a_1=A[0]\n a_n=A[n-1]\n b_1=B[0]\n b_n=B[n-1]\n\n if a_1!=0 or b_n!=0 or a_n!=b_1 :\n  ans="No"\n else:\n  for i in range(1,n-1):\n   if A[i]==0 or B[i]==0 :\n    ans="No"\n    break\n   elif b_1+A[i]<B[i]:\n    ans="No"\n    break\n   elif A[i]+B[i]<b_1:\n    ans="No"\n    break\n   elif B[i]+b_1<A[i]:\n    ans="No"\n    break\n   else:\n    pass\n\n print(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13429