Problem:
Weighted Union Find Trees

There is a sequence $A = a_0, a_1, ..., a_{n-1}$. You are given the following information and questions.

relate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$

diff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$

Input

$n \; q$
$query_1$
$query_2$
:
$query_q$

In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.

0 $x \; y\; z$

or

1 $x \; y$

where '0' of the first digit denotes the relate information and '1' denotes the diff question.

Output

For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.

Constraints

$2 \leq n \leq 100,000$

$1 \leq q \leq 200,000$

$0 \leq x, y < n$

$x \ne y$

$0 \leq z \leq 10000$

There are no inconsistency in the given information

Sample Input

5 6
0 0 2 5
0 1 2 3
1 0 1
1 1 3
0 1 4 8
1 0 4

Sample Output

2
?
10

Solution in Python3 (judge verdict: Wrong Answer)


n, q = map(int, input().split())

p = [i for i in range(n)]
rank = [0 for i in range(n)]
diff_weight = [0 for i in range(n)]


def link(x, y, z):
 if rank[x] > rank[y]:
  p[y] = x
  diff_weight[y] = z
 else:
  p[x] = y
  diff_weight[x] = -z
  if rank[x] == rank[y]:
   rank[y] = rank[y] + 1

def findSet(x):
 if x != p[x]:
  p[x] = findSet(p[x])
  diff_weight[x] += diff_weight[p[x]]
 return p[x]


def relate(x, y, z):
 rootx = findSet(x)
 rooty = findSet(y)
 z += diff_weight[x]
 z -= diff_weight[y]
 if rootx != rooty:
  link(rootx, rooty, z)


def same(x, y):
 x = findSet(x)
 y = findSet(y)

 if x == y:
  return 1
 else :
  return 0

def weight(x):
 findSet(x)
 return diff_weight[x]

def diff(x, y):
 if same(x, y) != 1:
  return '?'
 else :
  return diff_weight[y] - diff_weight[x]


output = []

for i in range(q):
 line = list(map(int, input().split()))

 if line[0] == 0:
  relate(line[1], line[2], line[3])

 else :
  output.append(diff(line[1],line[2]))
  #print(diff(line[1],line[2]))


for ans in output:
 print(ans)