Problem Statement

You are given a directed graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, ..., N$, and the edges are numbered $1, 2, ..., M$. Edge $i$ points from Vertex $a_i$ to Vertex $b_i$.

For each edge, determine whether the reversion of that edge would change the number of the strongly connected components in the graph.

Here, the reversion of Edge $i$ means deleting Edge $i$ and then adding a new edge that points from Vertex $b_i$ to Vertex $a_i$.

Constraints

• $2 \leq N \leq 1000$
• $1 \leq M \leq 200,000$
• $1 \leq a_i, b_i \leq N$
• $a_i \neq b_i$
• If $i \neq j$, then $a_i \neq a_j$ or $b_i \neq b_j$.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print $M$ lines. In the $i$-th line, if the reversion of Edge $i$ would change the number of the strongly connected components in the graph, print diff; if it would not, print same.