You $$are $$given $$an $$undirected $$graph $$consisting $$of $$

$$

$$vertices $$and $$

$$

$$edges$.$It $$is $$guaranteed $$that $$the $$given $$graph $$is $$connected $$

$($

i

$.$

$$e

$.$

$$it $$is $$possible $$to $$reach $$any $$vertex $$from $$any $$other $$vertex

$)$

$$and $$there $$are $$no $$self

$-$

loops $$

$($

$($

i

$.$

e

$.$

$$there $$is $$no $$edge $$between $$a $$node $$and $$itself$,$and $$no $$multiple $$edges $$in $$the $$graph $$

$($

i

$.$

e

$.$

$$if $$there $$is $$an $$edge $$between $$vertices $$

$$

$$

$,$

$$and $$

$$

$$

$,$

$$then $$it $$is $$only $$one $$edge

$)$

$.$

Your $$task $$is $$to $$calculate $$the $$number $$of $$simple $$paths $$of $$length $$at $$least $$

$2$

$$in $$the $$given $$graph$.$Note $$that $$paths $$that $$differ $$only $$by $$their $$direction $$are $$considered $$the $$same $$

$($

i

$.$

$$e

$.$

$$you $$have $$to $$calculate $$the $$number $$of $$undirected $$paths

$)$

$.$

$$For $$example$,$paths $$

$$

$1$

$,$

$$

$2$

$,$

$$

$3$

$$and $$

$$

$3$

$,$

$$

$2$

$,$

$$

$1$

$$are $$considered $$the $$same$.$

Recall $$that $$a $$path $$in $$the $$graph $$is $$a $$sequence $$of $$vertices $$

$$

$1$

$,$

$$

$2$

$,$

dots,

$$

$$

$$such $$that $$each $$pair $$of $$adjacent $$

$($

consecutive

$)$

$$vertices $$in $$this $$sequence $$is $$connected $$by $$an $$edge$.$The $$length $$of $$the $$path $$is $$the $$number $$of $$edges $$in $$it

$.$

$$A $$simple $$path $$is $$such $$a $$path $$that $$all $$vertices $$in $$it $$are $$distinct $$

$($

e

$.$

g

$.$

$$the $$path $$

$$

$1$

$,$

$$

$2$

$,$

$$

$3$

$,$

$$

$4$

$$is $$a $$simple $$path $$while $$the $$path $$

$$

$1$

$,$

$$

$2$

$,$

$$

$3$

$,$

$$

$2$

$,$

$$

$4$

$$is $$not $$a $$simple $$path $$because $$v

$2$

$$appears $$twice

$)$

$.$

The $$user $$inputs $$the $$number $$of $$vertices $$and $$the $$number $$of $$edges $$and $$then $$inputs $$edges $$in $$the $$form: $$

$$

$,$

$$

$($

$$i $$and $$

$$

$$are $$positive $$integers $$

$<=$

$$

$)$

$$to $$mean $$there $$is $$an $$edge $$between $$vertex $$i $$and $$vertex $$

$$

$.$