Score : $900$ points

Problem Statement

Consider making a string $s$ of length $N$ consisting of 0 and 1, where $s$ must satisfy $M$ conditions. The $i$-th condition is represented by integers $L_i$ and $R_i$ ($1 \leq L_i < R_i \leq N$). This means that there should be equal numbers of 0 and 1 between the $L_i$-th and $R_i$-th characters (inclusive) of $s$.

Find the lexicographically smallest string $s$ that satisfies all conditions. It can be proved that the Constraints of the problem guarantee the existence of $s$ that satisfies the conditions.

Constraints

• $2 \leq N \leq 10^6$
• $1 \leq M \leq 200000$
• $1 \leq L_i < R_i \leq N$
• $(R_i-L_i+1) \equiv 0 \mod 2$
• $(L_i,R_i) \neq (L_j,R_j)$ ($i \neq j$)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$L_1$ $R_1$

$L_2$ $R_2$

$\vdots$

$L_M$ $R_M$

Output

Print the answer.

4 2
1 2
3 4

0101

6 2
1 4
3 6

001100

20 10
6 17
2 3
14 19
5 14
10 15
7 20
10 19
3 20
6 9
7 12

00100100101101001011