Problem Statement

Consider a sequence of length $N$ consisting of 0s and 1s, $A=(A_1,A_2,\dots,A_N)$, that satisfies the following condition.

For every $i=1,2,\dots,M$, there are at least $X_i$ occurrences of 1 among $A_{L_i}, A_{L_i+1}, \dots, A_{R_i}$.

Print one such sequence with the fewest number of occurrences of 1s.

There always exists a sequence that satisfies the condition under the Constraints.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq \min(2 \times 10^5, \frac{N(N+1)}{2} )$
• $1 \leq L_i \leq R_i \leq N$
• $1 \leq X_i \leq R_i-L_i+1$
• $(L_i,R_i) \neq (L_j,R_j)$ if $i \neq j$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 X_1
L_2 R_2 X_2
\vdots
L_M R_M X_M

Output

Print a sequence $A$ consisting of 0s and 1s, with spaces in between.

A_1 A_2 \dots A_N

It must satisfy all the requirements above.