Count Two-Color Assignments

You are given an integer n and an array constraints, where constraints[i] = [t, a, b] links nodes a and b. There are n nodes labeled 1 to n, and each node must be assigned one of two colors:

• if t = 0, nodes a and b must get the same color;
• if t = 1, nodes a and b must get different colors.

Count the assignments of colors to all n nodes that satisfy every constraint, and return the count written in binary, as a string. If no assignment satisfies all constraints, return "0".

Examples

Example 1

Input: n = 3, constraints = [[0, 1, 2], [1, 3, 2]]
Output: "10"
Explanation: Node 2 must match node 1 and differ from node 3, so all three
nodes form one linked group with exactly two valid colorings (pick either
color for node 1 and the rest follows). The count is 2, which is "10" in
binary.

Example 2

Input: n = 4, constraints = [[1, 1, 2], [0, 2, 3], [1, 3, 4], [1, 1, 4]]
Output: "0"
Explanation: Following the first three constraints from node 1 forces node 4
to the same color as node 1, but the last constraint requires them to
differ. No assignment works.