In a town, there are n people labeled from 1 to n. There is a rumor that one of these people is secretly the town judge.

If the town judge exists, then:

1. The town judge trusts nobody.
2. Everybody (except for the town judge) trusts the town judge.
3. There is exactly one person that satisfies properties 1 and 2.

You are given an array trust where trust[i] = [aᵢ, bᵢ] representing that the person labeled aᵢ trusts the person labeled bᵢ. If a trust relationship does not exist in trust array, then such a trust relationship does not exist.

Return the label of the town judge if the town judge exists and can be identified, or return -1 otherwise.

Examples

Example 1

Input:  n = 2, trust = [[1,2]]
Output: 2

Example 2

Input:  n = 3, trust = [[1,3],[2,3]]
Output: 3

Example 3

Input:  n = 3, trust = [[1,3],[2,3],[3,1]]
Output: -1

Constraints

• 1 <= n <= 1000
• 0 <= trust.length <= 10^4
• trust[i].length == 2
• All pairs trust[i] are unique
• aᵢ != bᵢ
• 1 <= aᵢ, bᵢ <= n