Chef recently took a course in linear algebra and learned about linear combinations of vectors. Therefore, in order to test his intelligence, Raj gave him a "fuzzy" problem to solve.
A sequence of integers $B_1, B_2, \ldots, B_M$ generates an integer $K$ if it is possible to find a sequence of integers $C_1, C_2, \ldots, C_M$ such that $C_1 \cdot B_1 + C_2 \cdot B_2 + \ldots + C_M \cdot B_M = K$.
In this problem, Chef has a sequence $A_1, A_2, \ldots, A_N$ and he should answer $Q$ queries. In each query, he is given an integer $K$; the answer to this query is the number of pairs $(l, r)$ such that $1 \le l \le r \le N$ and the subsequence $(A_l, A_{l+1}, \ldots, A_r)$ generates $K$.
Chef has no idea how to solve this problem ― can you help him find the answers to all queries?

-----Input-----
- The first line of the input contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
- The third line contains a single integer $Q$.
- The following $Q$ lines describe queries. Each of these lines contains a single integer $K$.

-----Output-----
For each query, print a single line containing one integer ― the number of contiguous subsequences that generate $K$.

-----Constraints-----
- $1 \le N, Q \le 10^5$
- $1 \le A_i \le 10^9$ for each valid $i$
- $1 \le K \le 10^6$

-----Subtasks-----
Subtask #1 (10 points): $1 \le N \le 1,000$
Subtask #2 (90 points): original constraints

-----Example Input-----
2
2 4
3
1
2
8

-----Example Output-----
0
2
3

-----Explanation-----
The sequence $(2, 4)$ has three contiguous subsequences: $(2)$, $(4)$ and $(2, 4)$. 
- In the first query, $1$ cannot be generated by any subsequence.
- In the second query, $2$ is generated by subsequences $(2)$ and $(2, 4)$. For example, for the subsequence $(2, 4)$, we can choose $C_1 = 1$ and $C_2 = 0$.
- In the third query, $8$ is generated by all three subsequences.

```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 math\nn=int(input())\na=[int(i) for i in input().split()]\nop={}\ngcd={}\nfor i in a:\n gcd[i]=1\nwhile(len(a)!=0):\n newa=[]\n x=a[0]\n for i in a[1:]:\n  z=math.gcd(x,i)\n  try:\n   gcd[z]+=1\n  except:\n   gcd[z]=1\n  newa.append(z)\n  x=i\n a=newa\nfor i in gcd:\n j=i\n while(j<10**6+1):\n  try:\n   op[j]+=gcd[i]\n  except:\n   op[j]=gcd[i]\n  j+=i\nq=int(input())\nfor _ in range(q):\n try:\n  print(op[int(input())])\n except:\n  print(0)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 42643927