[python] How to concatenate two layers in keras?

I have an example of a neural network with two layers. The first layer takes two arguments and has one output. The second should take one argument as result of the first layer and one additional argument. It should looks like this:

x1  x2  x3
 \  /   /
  y1   /
   \  /
    y2

So, I'd created a model with two layers and tried to merge them but it returns an error: The first layer in a Sequential model must get an "input_shape" or "batch_input_shape" argument. on the line result.add(merged).

Model:

first = Sequential()
first.add(Dense(1, input_shape=(2,), activation='sigmoid'))

second = Sequential()
second.add(Dense(1, input_shape=(1,), activation='sigmoid'))

result = Sequential()
merged = Concatenate([first, second])
ada_grad = Adagrad(lr=0.1, epsilon=1e-08, decay=0.0)
result.add(merged)
result.compile(optimizer=ada_grad, loss=_loss_tensor, metrics=['accuracy'])

You can experiment with model.summary() (notice the concatenate_XX (Concatenate) layer size)

# merge samples, two input must be same shape
inp1 = Input(shape=(10,32))
inp2 = Input(shape=(10,32))
cc1 = concatenate([inp1, inp2],axis=0) # Merge data must same row column
output = Dense(30, activation='relu')(cc1)
model = Model(inputs=[inp1, inp2], outputs=output)
model.summary()

# merge row must same column size
inp1 = Input(shape=(20,10))
inp2 = Input(shape=(32,10))
cc1 = concatenate([inp1, inp2],axis=1)
output = Dense(30, activation='relu')(cc1)
model = Model(inputs=[inp1, inp2], outputs=output)
model.summary()

# merge column must same row size
inp1 = Input(shape=(10,20))
inp2 = Input(shape=(10,32))
cc1 = concatenate([inp1, inp2],axis=1)
output = Dense(30, activation='relu')(cc1)
model = Model(inputs=[inp1, inp2], outputs=output)
model.summary()

You can view notebook here for detail: https://nbviewer.jupyter.org/github/anhhh11/DeepLearning/blob/master/Concanate_two_layer_keras.ipynb

Adding to the above-accepted answer so that it helps those who are using tensorflow 2.0

import tensorflow as tf

# some data
c1 = tf.constant([[1, 1, 1], [2, 2, 2]], dtype=tf.float32)
c2 = tf.constant([[2, 2, 2], [3, 3, 3]], dtype=tf.float32)
c3 = tf.constant([[3, 3, 3], [4, 4, 4]], dtype=tf.float32)

# bake layers x1, x2, x3
x1 = tf.keras.layers.Dense(10)(c1)
x2 = tf.keras.layers.Dense(10)(c2)
x3 = tf.keras.layers.Dense(10)(c3)

# merged layer y1
y1 = tf.keras.layers.Concatenate(axis=1)([x1, x2])

# merged layer y2
y2 = tf.keras.layers.Concatenate(axis=1)([y1, x3])

# print info
print("-"*30)
print("x1", x1.shape, "x2", x2.shape, "x3", x3.shape)
print("y1", y1.shape)
print("y2", y2.shape)
print("-"*30)

Result:

------------------------------
x1 (2, 10) x2 (2, 10) x3 (2, 10)
y1 (2, 20)
y2 (2, 30)
------------------------------