Solve It

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

Given integers $p,q,r,s,t,u$, solve on $0\le x\le1$:

If no root exists, print No solution; otherwise print the root to four decimal places.

Input

The only line contains $p,q,r,s,t,u$.

Output

Print the root to four decimal places or No solution.

Subtasks

• Subtask 1 — 20%: $p=q=r=s=0$.
• Subtask 2 — 30%: $p,r\in[0,10]$, $q,s,t\in[-10,0]$.
• Subtask 3 — 50%: $0\le p,r\le20$, $-20\le q,s,t\le0$; $u$ is an integer.

Examples

Input

0 0 0 0 -2 1

Output

0.7071

Explanation

The equation becomes $-2x^2+1=0$, whose root in $[0,1]$ is approximately $0.7071$.