Problem: 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 $a_y$ $(a_y - a_x)$

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

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 $a_y$ $(a_y - a_x)$.

Example

Input

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


Output

2
?
10

Solution (in PYTHON3):

Solution:
import sys
import time
sys.setrecursionlimit(20000)

def find(tree,x):
    (idx,weight) = tree[x]
    if(idx== -1):
        return x
    else:
        root_idx = find(tree,idx)
        tree[x] = (root_idx, tree[x][1] + tree[idx][1])
        return root_idx

def relate(tree,x,y,z):
    x_root_idx = find(tree,x)
    y_root_idx = find(tree,y)
    if(x_root_idx == y_root_idx):
        return False
    
    if (tree_rank[y_root_idx] < tree_rank[x_root_idx]):
        tree[y_root_idx] = (x_root_idx, z+tree[x][1]-tree[y][1])
    else:
        tree[x_root_idx] = (y_root_idx, -z-tree[x][1]+tree[y][1])
        if(tree_rank[x_root_idx]==tree_rank[y_root_idx]):
            tree_rank[y_root_idx] = tree_rank[y_root_idx] + 1
    #tree[x_root_idx] = (y_root_idx,z-tree[x_root_idx][1]+tree[y_root_idx][1])

def diff(tree,x,y):
    x_idx = find(tree,x)
    y_idx = find(tree,y)
    if not(x_idx == y_idx):
        return "?"
    return tree[y][1] - tree[x][1]

if __name__ == '__main__':
    N,query_num = map(int, input().split())
    weighted_union_find_tree = [(-1,0) for _ in range(N)]
    tree_rank = [0]*N
    for i in range(query_num):
        query = list(map(int,input().split()))
        if(query[0]==0):
            relate(weighted_union_find_tree,query[1],query[2],query[3])
            #print(weighted_union_find_tree)
            #print(tree_rank)
        elif(query[0]==1):
            res = diff(weighted_union_find_tree,query[1],query[2])
            print(res)