+
0
y
y
+
s
x
y
s
+
x
y
++
nil
ys
ys
++
:
x
xs
ys
:
x
++
xs
ys
sum
:
x
nil
:
x
nil
sum
:
x
:
y
xs
sum
:
+
x
y
xs
sum
++
xs
:
x
:
y
ys
sum
++
xs
sum
:
x
:
y
ys
-
x
0
x
-
0
s
y
0
-
s
x
s
y
-
x
y
quot
0
s
y
0
quot
s
x
s
y
s
quot
-
x
y
s
y
length
nil
0
length
:
x
xs
s
length
xs
hd
:
x
xs
x
avg
xs
quot
hd
sum
xs
length
xs
2.2
sum
:
x
:
y
xs
sum
:
+
x
y
xs
length
:
x
xs
length
xs
avg
xs
sum
xs
sum
++
xs
:
x
:
y
ys
sum
:
x
:
y
ys
avg
xs
quot
hd
sum
xs
length
xs
avg
xs
hd
sum
xs
avg
xs
length
xs
sum
++
xs
:
x
:
y
ys
sum
++
xs
sum
:
x
:
y
ys
-
s
x
s
y
-
x
y
quot
s
x
s
y
-
x
y
sum
:
x
:
y
xs
+
x
y
+
s
x
y
+
x
y
sum
++
xs
:
x
:
y
ys
++
xs
sum
:
x
:
y
ys
++
:
x
xs
ys
++
xs
ys
quot
s
x
s
y
quot
-
x
y
s
y
true
avg
xs
length
xs
false
avg
xs
hd
sum
xs
false
avg
xs
quot
hd
sum
xs
length
xs
false
quot
s
x
s
y
quot
-
x
y
s
y
true
hd
1
0
s
1
1
23677
++
2
0
sum
1
0
avg
1
0
0
0
1
quot
2
0
:
2
0
++
2
0
nil
0
0
-
2
1
23676
avg
1
0
hd
1
0
-
2
0
quot
2
1
0
+
2
0
sum
1
0
length
1
0
length
1
0
+
2
0
-
x
0
x
-
s
x
s
y
-
x
y
-
0
s
y
0
avg
xs
sum
xs
false
length
:
x
xs
length
xs
true
hd
1
0
s
1
1
1
++
2
0
sum
1
0
avg
1
0
0
0
40651
quot
2
0
:
2
2
1
++
2
0
nil
0
0
-
2
1
23676
avg
1
0
hd
1
0
-
2
0
quot
2
1
0
+
2
0
sum
1
0
length
1
0
length
1
1
0
+
2
0
-
x
0
x
-
s
x
s
y
-
x
y
-
0
s
y
0
quot
s
x
s
y
-
x
y
false
-
s
x
s
y
-
x
y
true
hd
1
0
s
1
1
1
++
2
0
sum
1
0
avg
1
0
0
0
36466
quot
2
0
:
2
1
++
2
0
nil
0
0
-
2
1
0
avg
1
0
hd
1
0
-
2
1
2
0
quot
2
1
0
+
2
0
sum
1
0
length
1
0
length
1
0
+
2
0
-
x
0
x
-
s
x
s
y
-
x
y
-
0
s
y
0
sum
++
xs
:
x
:
y
ys
sum
++
xs
sum
:
x
:
y
ys
true
hd
1
0
s
1
1
1
++
2
1
2
40966
sum
1
3
avg
1
0
0
0
2998
quot
2
0
:
2
2
2
++
2
0
nil
0
1
-
2
1
0
avg
1
0
hd
1
0
-
2
0
quot
2
1
0
+
2
1
2
1
sum
1
1
0
length
1
0
length
1
0
+
2
0
++
:
x
xs
ys
:
x
++
xs
ys
-
x
0
x
+
0
y
y
++
nil
ys
ys
sum
:
x
nil
:
x
nil
-
s
x
s
y
-
x
y
sum
++
xs
:
x
:
y
ys
sum
++
xs
sum
:
x
:
y
ys
-
0
s
y
0
sum
:
x
:
y
xs
sum
:
+
x
y
xs
+
s
x
y
s
+
x
y
sum
++
xs
:
x
:
y
ys
++
xs
sum
:
x
:
y
ys
false
++
:
x
xs
ys
++
xs
ys
true
hd
1
0
s
1
1
1
++
2
1
2
42632
sum
1
57799
avg
1
0
0
0
2998
quot
2
0
:
2
2
1
++
2
1
0
nil
0
57798
-
2
1
0
avg
1
0
hd
1
0
-
2
0
quot
2
1
0
+
2
1
2
1
sum
1
1
0
length
1
0
length
1
0
+
2
0
++
:
x
xs
ys
:
x
++
xs
ys
-
x
0
x
+
0
y
y
++
nil
ys
ys
sum
:
x
nil
:
x
nil
-
s
x
s
y
-
x
y
sum
++
xs
:
x
:
y
ys
sum
++
xs
sum
:
x
:
y
ys
-
0
s
y
0
sum
:
x
:
y
xs
sum
:
+
x
y
xs
+
s
x
y
s
+
x
y
sum
++
xs
:
x
:
y
ys
sum
:
x
:
y
ys
false
sum
:
x
:
y
xs
sum
:
+
x
y
xs
true
hd
1
0
s
1
1
1
++
2
1
2
2831
sum
1
842
avg
1
0
0
0
12172
quot
2
0
:
2
2
1
++
2
0
nil
0
1
-
2
1
0
avg
1
0
hd
1
0
-
2
0
quot
2
1
0
+
2
1
2
50866
sum
1
1
0
length
1
0
length
1
0
+
2
0
++
:
x
xs
ys
:
x
++
xs
ys
-
x
0
x
+
0
y
y
++
nil
ys
ys
sum
:
x
nil
:
x
nil
-
s
x
s
y
-
x
y
sum
++
xs
:
x
:
y
ys
sum
++
xs
sum
:
x
:
y
ys
-
0
s
y
0
sum
:
x
:
y
xs
sum
:
+
x
y
xs
+
s
x
y
s
+
x
y
sum
:
x
:
y
xs
+
x
y
false
+
s
x
y
+
x
y
true
hd
1
0
s
1
1
1
++
2
1
2
2831
sum
1
842
avg
1
0
0
0
38145
quot
2
0
:
2
2
1
++
2
0
nil
0
1
-
2
1
0
avg
1
0
hd
1
0
-
2
0
quot
2
1
0
+
2
1
2
50866
sum
1
1
0
length
1
0
length
1
0
+
2
1
0
++
:
x
xs
ys
:
x
++
xs
ys
-
x
0
x
+
0
y
y
++
nil
ys
ys
sum
:
x
nil
:
x
nil
-
s
x
s
y
-
x
y
sum
++
xs
:
x
:
y
ys
sum
++
xs
sum
:
x
:
y
ys
-
0
s
y
0
sum
:
x
:
y
xs
sum
:
+
x
y
xs
+
s
x
y
s
+
x
y
NaTT
certifiable-1.6