Disjoint Set: Union Find Tree

Write a program which manipulates a disjoint set S = {S1, S2, . . . , Sk}.

First of all, the program should read an integer n, then make a disjoint set where each element consists of 0, 1, ... n−1 respectively.

Next, the program should read an integer q and manipulate the set for q queries. There are two kinds of queries for different operations:

• unite(x, y): unites sets that contain x and y, say Sx and Sy, into a new set.
• same(x, y): determine whether x and y are in the same set.

Constraints

• 1 ≤ n ≤ 10000
• 1 ≤ q ≤ 100000
• x ≠ y

Input

n q com1 x1 y1 com2 x2 y2 ... comq xq yq

In the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.

Output

For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.

Example

Input

5 12 0 1 4 0 2 3 1 1 2 1 3 4 1 1 4 1 3 2 0 1 3 1 2 4 1 3 0 0 0 4 1 0 2 1 3 0

Output

0 0 1 1 1 0 1 1

inputFormat

Input

n q com1 x1 y1 com2 x2 y2 ... comq xq yq

In the first line, n and q are given. Then, q queries are given where com represents the type of queries. '0' denotes unite and '1' denotes same operation.

outputFormat

Output

For each same operation, print 1 if x and y are in the same set, otherwise 0, in a line.

Example

Input

5 12 0 1 4 0 2 3 1 1 2 1 3 4 1 1 4 1 3 2 0 1 3 1 2 4 1 3 0 0 0 4 1 0 2 1 3 0

Output

0 0 1 1 1 0 1 1

样例

5 12
0 1 4
0 2 3
1 1 2
1 3 4
1 1 4
1 3 2
0 1 3
1 2 4
1 3 0
0 0 4
1 0 2
1 3 0

0
0
1
1
1
0
1
1

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