Count all edges

I am wondering is there any good way to count all edges.
schema is simple:

node1: string @index(exact) .
node2: string @index(exact) .
node3: string @index(exact) .
rela1: [uid] @count .
rela2: [uid] @count .
rela3: [uid] @count .


# nodes
_:x1 <node1> "a1" .
_:x1 <node2> "b1" .
_:x1 <node3> "c1" .
_:x2 <node1> "a2" .
_:x2 <node2> "b2" .
_:x2 <node3> "c2" .
_:x3 <node1> "a3" .
_:x3 <node2> "b3" .
_:x3 <node3> "c3" .

# edges
_:x1 <rela1> _:x2 .
_:x1 <rela2> _:x2 .
_:x1 <rela3> _:x2 .
_:x2 <rela1> _:x1 .
_:x2 <rela2> _:x1 .
_:x2 <rela3> _:x1 .
_:x3 <rela1> _:x1 .
_:x3 <rela2> _:x1 .

I want to count all edges (including rela1, rela2, rela3)
Below codes do work, but just for single edge, how can I calculate all edges, by using type function (avoiding “has” to save time)

  var(func: has(rela1)) {
    c as count(rela1)
	  Cul() {
   total:  sum(val(c))

You may use some DQL query like this

  var(func: type(/*Type of node*/)) {
    c as count(rela1)
    d as count(rela2)
    e as count(rela3)
    f as math(c+d+e)
	  Cul() {
   total_edges: sum(val(f))