Lone Wolf and Cub: Baby Cart at the River Styx

In this second Lone Wolf and Cub movie, the disgraced former executioner, or Kogi Kaishakunin to the shogun, Ogami Itto is now living rough on the land with his three-year-old son Daigoro, travelling the countryside as a hired killer. Pushing his son in a baby cart, he stops at a bathhouse looking for a room and a bath, and is eagerly welcomed in by a young woman. However, the manager of the house sees Itto as a dirty vagabond and scolds the young woman for letting him in the house. Overhearing this, Itto goes to the baby cart and retrieves a bundle and hands it to the manager for safe keeping it is 500 gold pieces, earned from a recent job. The manager's tone quickly changes, but when he tries to wash Daigoro's feet, the boy kicks water at the old man and tromps across the floor, leaving wet footprints.Itto's activities are being watched by the Kurokawa spy clan of Shinobi-class ninja, which have fallen in with Itto's nemesis, the Shadow Yagyu. They report on his activities to Sayaka, head of Akari Yagyu clan of female assassins. But the Kurokawa are unsure that the women are up to the task of killing Itto. Sayaka laughs confidently and tells the Kurokawas' leader to send their best man into the room. She then orders the man to try and exit the room. He tries to do so by grappling onto the ceiling, but the female assassins set upon him and make short work of him, hacking off his ears, fingers, arms and legs, leaving the man a writhing heap of just a torso and head before he is finally finished off.Itto, meanwhile, is hired by a clan that specializes in making indigo dye and has a secret process. One of the clan plans to sell out the secret to the shogun. Itto must kill him. The turncoat will be escorted by the three Hidari brothers, each a master of a deadly weapon; the iron claw, the flying mace, and a pair of armored gloves.As he travels to his job, Itto encounters three groups of female assassins of the Akari clan. The first group is disguised as an acrobat troupe that turns deadly as their gymnastic moves are combined with blades and turned against Itto. He then encounters a pair of women who with blades on their straw hats that they throw at Itto as if they are Frisbees. Finally, some women washing vegetables by the river turn out to be assassins and the daikons they are washing are wielded as weapons. Itto kills them all.Then he meets Sayaka, who catches him, his son and the baby cart in a steel net. Itto cuts his way out of the net and engages in a sword duel with her. He delivers what should be a disabling blow to her ankles, but the woman fighter jumps straight up out of her kimono to reveal a fishnet body suit and then runs away, bizarrely jogging backwards.Next, the Kurokawa clan are waiting for Itto, who puts together his naginata (disguised as railing on the baby cart) and gives the baby cart a shove toward the waiting enemies. Daigoro, still in the baby cart then activates blades in the axles of the cart, which cut off the feet of several men. The battle that ensues between Itto and the Kurokawas is fierce and Itto is injured before he kills them all.Weary from the endless fighting, Itto struggles along the road and eventually finds shelter in a shack. Daigoro, seeing that his father needs his help, must do what he can. Unable to carry water in his tiny hands, Daigoro carries water from the river in the only vessel available his mouth. He spits the few drops he could carry between his father's parched lips. For food, Daigoro finds some rice cakes given as an offering to a Buddha statue and takes them for his father, leaving his vest in exchange. Itt recovers and finds that his son is missing. Daigoro has been taken by the Kurokawa and Sayaka, tied up and suspended over a water well. If Itto attacks, they will let go of the rope and Daigoro will plunge to his death. Daigoro lets his sandal drop into the well, giving Itt a gauge of how deep it is. He then makes his move as the rope unspools, stopping it just in time.Sayaka watches silently and makes no move to engage the swordsman, realising his technique far outstrips her own and perhaps also out of a sense of honor for the devotion of the father to his child.Itto then finds himself aboard a ship, carrying the three Hidari brothers. Itto is met by several other members of the indigo-dye clan, who try to kill the Hidaris but are bloodily rebuffed. The clan then sets the ship on fire in an attempt to kill the Hidaris, but the three killers escape. Itto tosses Daigoro and the baby cart into the water, the cart proves itself by floating.Sayaka has followed Itto onto the ship and in the water, she tries to kill him, but is disarmed. Itto, with Daigoro and Sayaka, find shelter, but they are cold. Itt disrobes himself and Daigoro, then turns on Sayaka, tearing off her clothes. But he does not mean to rape her. Instead, he is seeking to get her out of her cold, wet clothes and cling to her while nude. "Three people are warmer than two," he explains. She thinks about taking his sword and killing him, but the cozy scene, with Daigoro sitting between them, playfully fondling her breast, makes her abandon the plan.The final showdown takes place on a vast area of sand dunes. The three Hidari brothers are at the head of a caravan of men carrying a palanquin with the indigo expert inside. The brother with the iron claw runs forward and thrusts his claw into the sand, which boils up with blood. There are men hiding in the sand. He digs his claw into the sand several times, each time creating a pool of blood and pulling up a hiding warrior by his head. The rest of the hidden men in the sand emerge and fight, but the Hidari brothers dispatch them all.Itto awaits, alone, at the top of a large dune. Each brother is dispatched in a high-pressure spray of blood, with the last brother dispatched in a lethal stroke along the throat, a cut that sprays blood in a fine mist, while making a sound like the "howling of the wind". The final slain Hidari brother comments such a fabled finishing stroke is referred to as "Mogaribue", and wishes he had heard the sound just once from the many people he has killed, but is instead hearing it from his own neck as his life slowly drains away.Itto approaches the palanquin with the traitorous indigo expert inside, finishing him off before gathering Daigoro and again setting off. The end sees them out of the desert and on a coastal trail, followed by Sayaka. Aware of her presence Itto stops the cart, looking straight ahead whilst holding out his dotanuki blade, as Sayaka wielding a katana is revealed behind him. Itto stands ominously still until he hears the sound of Sayaka dropping her sword; knowing that she can never defeat the master swordsman.

Question: What does Daigoro leave in exchange for the rice cakes he takes for his father?
Answer: His vest